Mat540 Homework Week 1 Chapter

Mat540 Homework Week 1 Chapter

Determine the core assignment questions: The assignment involves solving a series of problems related to cost analysis, break-even points, expected values, probability calculations, and decision-making based on statistical data in various business scenarios. It includes calculating costs, revenues, profits, break-even volumes, the impact of price and expenditure changes, expected grades, investment choices, probabilities in normal distributions, and inventory management for demand fulfillment.

Remove extraneous information such as repetitive lines, unrelated dialogue, or interview forms. Focus only on the math and business analysis questions: calculations of costs, revenues, break-even points, probabilities, expected values, variances, and decision-making based on statistical and financial data.

Paper For Above instruction

The comprehensive analysis of business scenarios presented in this assignment highlights the importance of calculating costs, revenues, and break-even points to inform strategic decision-making. By evaluating various scenarios, companies can optimize their operations, pricing strategies, and inventory management to maximize profitability and efficiency.

In the first scenario involving The Retread Tire Company, fixed and variable costs are key to understanding total costs and profits at a given volume. The fixed annual cost is $55,000, with a variable cost of $8 per tire, and a selling price of $21 per tire. For an annual volume of 10,000 tires, the total cost is computed as:

Total Cost = Fixed Costs + (Variable Cost × Volume) = $55,000 + ($8 × 10,000) = $55,000 + $80,000 = $135,000.

The total revenue at this volume is:

Total Revenue = Selling Price × Volume = $21 × 10,000 = $210,000.

Therefore, the profit is:

Profit = Total Revenue – Total Cost = $210,000 – $135,000 = $75,000.

The break-even volume is where total revenue equals total costs. Solving for volume (V):

Revenue = Cost, so:

$21V = $55,000 + $8V

Rearranged as:

$21V – $8V = $55,000

$13V = $55,000

V = $55,000 / $13 ≈ 4231 tires.

Moving to fertilization, Evergreen Fertilizer’s monthly fixed costs are $30,000, with variable costs of $0.16 per pound, and a selling price of $0.40 per pound. The break-even volume in pounds per month is determined by:

Fixed Costs / (Selling Price – Variable Cost) = $30,000 / ($0.40 – $0.16) = $30,000 / $0.24 ≈ 125,000 pounds.

If the price increases to $0.60 per pound, then the break-even volume reduces to:

$30,000 / ($0.60 – $0.16) = $30,000 / $0.44 ≈ 68,182 pounds.

The increase in price significantly reduces the necessary volume to cover fixed costs, directly influencing profitability and sales strategies.

Similarly, increasing advertising expenditures by $14,000 annually raises total fixed costs to $44,000. The new break-even volume at a $0.40 per pound price becomes:

$44,000 / ($0.40 – $0.16) = $44,000 / $0.24 ≈ 183,333 pounds.

This higher volume requirement emphasizes the need for effective marketing and sales strategies to meet increased fixed costs.

In the case of Annie McCoy’s hot dog stand, fixed costs include a vendor fee of $2,500 and equipment costs of $3,100, totaling $5,600 for the season. Each hot dog costs $0.35 to produce, and the sales volume per game is estimated at 2,000 hot dogs. To find the break-even price, the total costs are divided among the expected number of hot dogs sold:

Total costs = $2,500 + $3,100 = $5,600.

Break-even price = Total costs / Number of hot dogs sold per game = $5,600 / 2,000 = $2.80 per hot dog.

Factors affecting actual sales and pricing include weather conditions affecting attendance, competitor pricing, and changes in consumer preferences, which could influence actual volume sold and necessitate price adjustments.

The online MBA program's financial analysis involves calculating the required enrollment to recover a $360,000 initial investment with tuition of $17,000 per student. The university’s share reduces the net revenue per student to $5,000 ($17,000 – $12,000). The breakeven number of students is:

$360,000 / $5,000 = 72 students.

If only 75 students enroll, the profit is:

(75 – 72) × $5,000 = 3 × $5,000 = $15,000.

Increasing tuition to $22,000, while reducing enrollment to 72 students, would increase gross revenue but might reduce overall profit due to decreased enrollment, potentially affecting the program’s viability and marketability.

Decision-making under uncertainty, such as grades' expected value and variance, provides insights into academic performance. Assigning GPA points based on letter grades with given probabilities, the expected grade is calculated as:

E(GPA) = Σ (Grade Point × Probability) = (4.0 × 0.15) + (3.0 × 0.25) + (2.0 × 0.38) + (1.0 × 0.12) + (0.0 × 0.00) = 0.6 + 0.75 + 0.76 + 0.12 + 0.00 = 2.23.

The variance is derived from the squared deviations weighted by the probabilities.

Investment choices are evaluated based on expected values under different economic conditions, where investment A may result in a gain or loss, and similarly for B. Calculating the expected value:

Expected value (A) = (0.60 × $350,000) + (0.40 × –$350,000) = $210,000 – $140,000 = $70,000.

Expected value (B) = (0.60 × $120,000) + (0.40 × $70,000) = $72,000 + $28,000 = $100,000.

With higher expected return, Investment B is preferable under these assumptions.

The probability of a fertilizer bag weighing between 45 and 55 pounds assuming normal distribution with mean 50 and SD 7 can be calculated using standard normal tables or Z-scores:

Z = (X – μ) / σ.

For X=45, Z = (45 – 50)/7 ≈ –0.714; similarly for 55, Z ≈ 0.714.

Using standard normal distribution, the probability between Z=–0.714 and Z=0.714 is approximately 48.7 %.

This probabilistic modeling assists in quality control and inventory management.

The probability that the shopping center is not ready by 19 months, given an expected time of 16 months and SD of 4 months, can be found via the Z-score:

Z = (19 – 16)/4 = 0.75.

Using standard normal tables, the probability that the project exceeds 19 months is 1 – P(Z ≤ 0.75) ≈ 1 – 0.7734 = 0.2266, or about 22.7 %.

Finally, inventory decisions for recorders involve determining the stock level that meets 90% of demand, modeled by normal distribution with mean 180 and SD 60. The Z-value for 90% confidence is approximately 1.28. Applying this:

Order quantity = Mean + Z × SD = 180 + 1.28 × 60 ≈ 180 + 76.8 ≈ 257 recorders.

This ensures meeting approximately 90% of customer demand, balancing cost and service level.

References

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