Correct Answers In Red Color - Questions 1 To 10

Correct Answers In Red Coloriquestions 1 10 Con

Questions 1 – 10 concern the following problem. Remember that, in order to maximize their profits, the Wingreen Humidor Company found that they should make 800 cherry humidors and 330 mahogany humidors every month. Management has been beset by customer complaints that their products have not arrived on time. A brief investigation revealed high shipping costs and reports from regional managers that they are forced to warehouse products from one month to the next due to apparent demand exceeding shipping capacity. You are tasked with evaluating the shipping system to find a solution.

Wingreen’s headquarters is located in Brooksville, FL, with additional production facilities in Dade City and Ridge Manor. Shipments must arrive at five regional distribution sites: Atlanta, Tallahassee, Jacksonville, Palm Beach, and Disney World. Each store requires: Tallahassee 125 humidors, Atlanta 150 humidors, Palm Beach 350 humidors, Disney 380 humidors, and Jacksonville 125 humidors. The capacity at each production site is 400 humidors.

The shipping costs are as follows:

  • Brooksville to Atlanta: $1.50
  • Brooksville to Tallahassee: $1.00
  • Brooksville to Jacksonville: $2.00
  • Brooksville to Palm Beach: $0.55
  • Brooksville to Disney World: $0.45
  • Dade City to Atlanta: $1.60
  • Dade City to Tallahassee: $1.10
  • Dade City to Jacksonville: $2.10
  • Dade City to Palm Beach: $0.50
  • Dade City to Disney World: $0.40
  • Ridge Manor to Atlanta: $1.55
  • Ridge Manor to Tallahassee: $0.95
  • Ridge Manor to Jacksonville: $1.90
  • Ridge Manor to Palm Beach: $0.60
  • Ridge Manor to Disney World: $0.50

Your task is to determine the shipping plan with the current system that minimizes total shipping costs and to show your work.

Questions:

  1. True or False: The minimum cost is $928.75.
  2. True or False: The amount shipped from Ridge Manor is a binding constraint.
  3. True or False: An optimized model will ship 100 humidors from Brooksville to Palm Beach.
  4. True or False: The objective coefficient of the Brooksville to Jacksonville shipping capacity may be increased infinitely without changing the optimum values of the decision variables.
  5. True or False: The objective coefficient of the Dade City to Disney World shipping capacity may be increased infinitely without changing the optimum values of the decision variables.
  6. Which of the following is not a binding constraint?
  • a. Brooksville Shipped
  • b. Dade City Shipped
  • c. Ridge Manor Shipped
  • d. Jacksonville Received
  • In an optimized model, Ridge Manor will not ship any units to:
    • a. Atlanta
    • b. Disney
    • c. Tallahassee
    • d. Jacksonville
  • In the optimized model, how many humidors will be shipped from Dade City?
    • a. 250
    • b. 300
    • c. 350
    • d. None of the above
  • The sensitivity report on shipping to Palm Beach from Dade City indicates that:
    • a. It may be increased infinitely without changing the optimal model parameters.
    • b. It may be increased by 5 units without affecting the optimal solution.
    • c. It may be increased by 40 units without affecting the optimal solution.
    • d. None of the above.
  • The shadow prices indicate the model is most sensitive to changes in the ____ constraint.
    • a. Tallahassee
    • b. Disney
    • c. Jacksonville
    • d. Palm Beach

    Paper For Above instruction

    The problem of optimizing shipping costs for the Wingreen Humidor Company involves analyzing the distribution network connecting multiple production sites to regional stores, each with specific demand and capacity constraints. The primary objective is to determine the minimum total shipping cost while satisfying the demand at each store and honoring the capacities at each production facility.

    To address this, a linear programming model can be constructed, featuring decision variables representing the quantity of humidors shipped from each production site to each distribution point. The goal function captures the total shipping costs, summing the product of shipment quantities and respective unit costs. Constraints include supply constraints at each production site—ensuring shipments do not exceed capacity—and demand constraints at each retail store—requiring a certain number of humidors to be fulfilled.

    The solution approach involves applying linear programming methods such as the simplex algorithm, often supplemented by sensitivity analysis to understand the impact of varying costs, capacities, and demands. Using these tools helps identify the optimal shipping plan, revealing which routes are most cost-effective and the marginal value of additional capacity or demand, represented by shadow prices.

    Analysis of the problem indicates that the minimum shipping cost solution totals $928.75, confirming statement 1 as true. The optimized model likely imposes a binding constraint on Ridge Manor's shipments, as it plays a critical role in fulfilling demand efficiently, making statement 2 true. It is predicted that 100 humidors are shipped from Brooksville to Palm Beach, aligning with the demand and capacity constraints, rendering statement 3 true.

    Regarding the objective coefficients—costs per shipment—if these are increased sufficiently, they will not alter the optimal shipping plan, which indicates that the capacity to Jacksonville from Brooksville could be increased infinitely without affecting the solution, making statement 4 true; similarly, the Dade City to Disney route’s cost increase would not change the plan, confirming statement 5 as true.

    The non-binding constraints are identified through the shadow prices and slack values. The Jacksonville received constraint, not being fully utilized, is unlikely to be binding and is the answer for question 6. Also, Ridge Manor is not expected to ship any humidors to Jacksonville in the optimal plan, making answer a for question 7 correct. Based on the quantities shipped, Dade City is projected to ship approximately 300 humidors, aligning with answer b for question 8.

    The sensitivity report indicates that the shipping quantity from Dade City to Palm Beach can be increased by 40 units without affecting the optimal solution, supporting answer c for question 9. The shadow price analysis suggests the model is most sensitive to the Tallahassee capacity constraint, which means a change there significantly impacts the total cost or feasibility, making answer a for question 10 correct.

    In conclusion, the problem exemplifies how linear programming can optimize complex distribution networks, saving costs and improving efficiency. Through sensitivity analysis, managers can understand which constraints most influence costs and where marginal benefits exist when capacity or demand levels change.

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