Da Quiz Question 1: 3 Points Assume That A Company Makes Woo

Da Quizquestion 1 3 Pointsassume That A Company Makes Wooden Picture

Assume that a company makes wooden picture frames. Frame style 1 takes 2 hours of skilled labor and 3 linear feet of wood. If the company had 40 hours of skilled labor and 48 linear feet of wood that can be used each week, what is the largest quantity of this item that the company will be able to produce given these resource constraints?

Question 1 options: Save Question 2 (3 points) Every linear programming problem involves optimizing a: Question 2 options: linear regression model subject to several linear constraints linear function subject to several linear constraints linear function subject to several non-linear constraints non-linear function subject to several linear constraints Save Question 3 (3 points) Related to sensitivity analysis in linear programming, when the profit increases with a unit increase in a resource, this change in profit is referred to as the: Question 3 options: add-in price sensitivity price shadow price additional profit Save Question 4 (3 points) Consider the following linear programming problem: Maximize 5x1 + 5x2 Subject to x1 + 2x2 0 What is the optimal objective function value? Question 4 options: Save Question 5 (3 points) One of the things that can go wrong with a linear programming problem is that it may not be possible to find a set of points that satisfy all of the constraints in the problem. This type of problem is said to be: Question 5 options: infeasible inconsistent unbounded redundant Save Question 6 (3 points) In using a spreadsheet to solve linear programming problems, the changing cells represent the: Question 6 options: value of the objective function constraints decision variables total cost of the model Save Question 7 (3 points) In using a spreadsheet to solve linear programming problems, the target cell represents the: Question 7 options: value of the objective function constraints decision variables total cost of the model Save Question 8 (3 points) In binary integer linear program, the integer variables take only the values: Question 8 options: 0 or 1. 0 or ∞. 1 or ∞. 1 or –1. Save Question 9 (3 points) Binary variables are identified with the _____designation in the Solver Parameters dialog box. Question 9 options: bin 0 and 1 int dif Save Question 10 (5 points) Questions are based on the following information: A farmer in Egypt owns 50 acres of land. He is going to plant each acre with cotton or corn. Each acre planted with cotton yields $400 profit; each with corn yields $200 profit. The labor and fertilizer used for each acre are given in the table below. Resources available include 150 workers and 200 tons of fertilizer. Cotton Corn Labor (Workers) Fertilizer (Tons) Formulate a linear programming model that will enable the farmer to determine the number of acres that should be planted cotton and/or corn in order to maximize his profit. Provide the objective function and constraints in the box below. X1 - number of acres planted cotton X2 - number of acres planted corn Hint: You will need three constraints. Question 10 options: Save Question 11 (4 points) What are the optimal decision variable values? Question 11 options: X1 = 30 X2 = 0 X1 = 0 X2 = 30 X1 = 40 X2 = 0 X1 = 0 X2 = 40 Save Question 12 (4 points) What is the optimal objective function value? Question 12 options: $13,000 $12,000 $14,000 $15,000 Save Question 13 (4 points) Which of the following constraints is binding? Question 13 options: Labor Fertilizer Land None Save Question 14 (4 points) How much should the farmer be willing to pay for an additional worker? Question 14 options: Save Question 15 (4 points) How much should the farmer be willing to pay for an additional ton of fertilizer? Question 15 options: $0 $80 $60 $40 Save Question 16 (5 points) Questions are based on the following information: Dukedom Chemicals blends its private label orchard spray from four individual compounds. Management would like to make the blend at as low a cost as possible while maintaining the requirements for chemical structure. The linear programming problem has been formulated and the SOLVER solution to it is provided. The objective function is to minimize the total cost. The two constraints are formulated to meet the minimum requirements for chemicals 1 and 2. What is the total cost to make the blend? Question 16 options: Save Question 17 (4 points) How many units of compound 4 should we use? Question 17 options: 5. Save Question 18 (4 points) What would happen to the decision variables if the cost of compound 2 were $15? Question 18 options: $15 is outside the range of optimality and we have to resolve the problem. $15 is inside the range of optimality and the new optimal decision variables will decrease. $15 is inside the range of optimality and the new optimal decision variables stay the same. $15 is inside the range of optimality and the new optimal decision variables will increase. Save Question 19 (4 points) What would happen if 1 more unit of chemical 1 were required in constraint (1)? Question 19 options: It is outside the range and we have to resolve the problem to know the new total cost. It will increase the total cost by $0.6667. It will decrease the total cost by $0.6667. None of the above. Save Question 20 (4 points) Which of the constraints is binding? Question 20 options: Constraint (1) Constraint (2) Neither. None of the above Save P1–6 ETHICS PROBLEM What does it mean to say that managers should maximize shareholder wealth “subject to ethical constraints”? What ethical considerations might enter into decisions that result in cash flow and stock price effects that are less than they might otherwise have been? E2–4 Your broker calls to offer you the investment opportunity of the lifetime, the chance to invest in mortgage-backed securities. The broker explains that these securities are entitled to the principal and interest payments received from a pool of residential mortgages. List some of the questions you would ask your broker so as to assess the risk of this investment opportunity. P2–1 Corporate taxes Tantor Supply, Inc., is a small corporation acting as the exclusive distributor of a major line of sporting goods. During 2013, the firm earned $92,500 before taxes. a. Calculate the firm’s tax liability using the corporate tax rate schedule given in Table 2.1. b. How much are Tantor Supply’s 2013 after-tax earnings? c. What was the firm’s average tax rate, based on your findings in part a? d. What was the firm’s marginal tax rate, based on your findings in part a? P2–4 Interest versus dividend income During the year just ended, Shering Distributors, Inc., had pretax earnings from operations of $490,000. In addition, during the year it received $20,000 in income from interest on bonds it held in Zig Manufacturing and received $20,000 in income from dividends on its 5% common stock holding in Tank Industries, Inc. Shering is in the 40% tax bracket and is eligible for a 70% dividend exclusion on its Tank Industries stock. a. Calculate the firm’s tax on its operating earnings only. b. Find the tax and the after-tax amount attributable to the interest income from Zig Manufacturing bonds. c.

Find the tax and the after-tax amount attributable to the dividend income from the Tank Industries, Inc., common stock. d. Compare, contrast, and discuss the after-tax amounts resulting from the interest income and dividend income calculated in parts b and c. e. What is the firm’s total tax liability for the year? CH1- Cost Benefit Formulas Monsanto Corporation Purchase of New Equipment Cost-Benefit Analysis Benefits with the new equipment $ 900,000 Less: Benefits with the old equipment 300,000 Marginal (added) benefits of the New Equipment $600,000 Cost of new equipment $ 600,000 Less: Proceeds from the sale of the old equipment 250,000 Marginal (added) costs of the New Equipment $ 350,000 Net benefit of the proposed purchase of new equipment $250,000 CH2 Corp Taxes Formulas Current Income Expansion Income Expansion Income With No Expansion Using Cash Reserves Using Debt Financing Before tax income $200,000 $350,000 $350,000 Corporate Tax Rate Schedule Interest expense $0 $0 $70,000 Taxable income $200,000 $350,000 $280,000 Range of taxable income Marginal tax rate x Amount over base bracket Amount over base bracket Amount over base bracket $0 to $50,% x $7,500 $7,500 $7,500 $50,000 to $75,% x $6,250 $6,250 $6,250 $75,000 to $100,% x $8,500 $8,500 $8,500 $100,000 to $335,% x $39,000 $91,650 $70,200 $335,000 to $10,000,% x $5,100 $10,000,000 to $15,000, % x $15,000,000 to $18,333, % x $18,333,333 over 35% x Total corporate tax liability $61,250 $119,000 $92,450 Average corporate tax rate 30.63% 34.00% 33.02%

Sample Paper For Above instruction

In today's competitive business environment, effective resource allocation is paramount for maximizing profitability and operational efficiency. Linear programming (LP) emerges as a critical mathematical tool that enables managers to optimize decision variables within constrained resources. This paper explores the concept of linear programming, its key components, and practical applications through real-world examples, emphasizing its significance in strategic planning and decision-making.

Understanding Linear Programming

Linear programming is a mathematical technique used to determine the best possible outcome—such as maximum profit or minimum cost—given a set of linear constraints. The core idea involves optimizing a linear objective function, which represents the goal of the decision-maker, subject to various constraints that limit the possible solutions. These constraints typically include resource limitations, technological limitations, or policy restrictions, all expressed as linear inequalities or equations. The importance of LP lies in its ability to handle multiple variables and constraints simultaneously, providing a systematic approach to complex decision problems.

Key Components of Linear Programming

The main elements of a linear programming model include decision variables, the objective function, and constraints. Decision variables are the controllable inputs, such as the number of units to produce or resources to allocate. The objective function quantifies the goal, for example, maximizing profit or minimizing costs, and is expressed as a linear combination of the decision variables. Constraints define the limits within which decision variables must operate and are also expressed linearly. Additionally, LP models often incorporate non-negativity constraints, ensuring variables do not assume negative values.

Applications and Examples

Linear programming has widespread applications across industries. For instance, in manufacturing, companies like a wooden picture frame producer must determine the optimal mix of frame styles to maximize output given limited labor and materials. As outlined in the initial problem, resources such as skilled labor hours and wood length impose constraints on production levels. The solution involves setting decision variables for each product style, formulating an objective function for profit maximization, and defining resource constraints. Solving this LP model helps identify the quantity of each product to produce, ensuring resource utilization is maximized without exceeding limits.

Resource Constraints and Optimization

The utility of LP extends beyond manufacturing. In agriculture, a farmer seeks to allocate land among crops like cotton and corn, considering profit margins and resource limitations such as labor and fertilizer. Formulating this scenario involves defining decision variables for acres allocated to each crop, setting an objective function to maximize profit, and establishing constraints based on available labor, fertilizer, and total land. Solving such models facilitates optimal crop planting strategies that enhance profitability while adhering to resource constraints.

Sensitivity Analysis and Decision-Making

Sensitivity analysis is an integral part of LP, providing insights into how changes in resource availability or profit margins impact optimal solutions. For example, if the cost of an input increases or decreases, or if the value of a resource’s shadow price fluctuates, managers can assess whether to adjust production plans. Understanding the shadow prices or dual variables helps identify which constraints are binding, guiding managerial decisions regarding resource investment or cost negotiations.

Limitations and Challenges

Despite its strengths, linear programming has limitations. It assumes linearity in relationships and constraints, which may not always reflect reality where non-linear interactions exist. Additionally, LP models may become infeasible if constraints conflict, or unbounded if the objective can be increased infinitely without constraints. Accurate data collection and model formulation are crucial; errors can lead to suboptimal or invalid solutions. Nevertheless, LP remains a vital tool in operations research, aiding decision makers in optimizing complex systems efficiently.

Conclusion

Linear programming plays a vital role in strategic decision-making across industries by providing a structured method to maximize or minimize objectives within resource constraints. Its ability to integrate multiple variables, constraints, and sensitivities makes it indispensable for planning and operational efficiency. As businesses continue to seek competitive advantages, mastery of LP and related analytical tools will be increasingly valuable for sustainable growth and innovation.

References

• Hillier, F. S., & Lieberman, G. J. (2015). Introduction to Operations Research. McGraw-Hill Education.
• Taha, H. A. (2017). Operations Research: An Introduction. Pearson.
• Winston, W. L. (2004). Operations Research: Applications and Algorithms. Thomson/Brooks/Cole.