CSU COMP480 HOMEWORK 6

BUS 190

Homework 6 Solutions

1. Tom’s Inc. makes two salsa products: Western Foods salsa and Mexico City salsa. Essentially, the two products have different blends of whole tomatoes, tomato sauce, and tomato paste. A jar of Western Foods salsa uses 5 ounce of whole tomatoes, 3 ounces of tomato sauce, and 2 ounces of tomato paste. A jar of Mexico City salsa consists of 7 ounces of whole tomatoes, 1 ounce of tomato sauce, and 2 ounces of tomato paste.

For the current production period Tom’s Inc. can purchase up to 4480 ounces of whole tomatoes, 2080 ounces of tomato sauce, and 1600 ounces of tomato paste. Tom’s Inc. makes a profit of $1.00 per jar of Western Foods salsa and $1.25 per jar of Mexico City salsa.

The following linear programming model was used to determine the mix of salsa products that will maximize the total profit contribution.

W = Jars of Western Foods Salsa

M = Jars of Mexico City Salsa

Maximize 1W + 1.25M

Subject to

5W + 7M? 4480 (Whole tomatoes)

3W + 1M? 2080 (Tomato sauce)

2W + 2M? 1600 (Tomato paste)

W,M? 0

The problem was solved in Excel and the sensitivity report is shown on the next page.

Microsoft Excel 11.0 Sensitivity Report

Adjustable Cells

a) What are the optimal production quantities?

b) What is the profit of the optimal solution?

c) Which constraints are binding?

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d) Which would be more valuable, an additional ounce of whole tomatoes or an additional ounce of tomato paste?

e) How much less profit would Tom’s make if they had 200 fewer ounces of tomato sauce?

f) How would Tom’s profit change if they had 100 more ounces of whole tomatoes?

2. Tri-County Utilities Inc. supplies natural gas to customers in a three county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Hamilton County, 400 units; Butler County, 200 units; and Clermont

County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon thelocation of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows:

a) Draw a network representation of this problem.

b) Formulate a transportation model that can be used to determine the plan that will minimize total distribution costs.

c) Use Excel to solve the problem. State the optimal distribution plan and the total distribution costs. Please turn in your spreadsheet as well.

Please see the spreadsheet online for the model.

3. An air-conditioning manufacturer produces room air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to regional distributors in Dallas, Atlanta, and Denver. The shipping costs vary, and the company would like to find the least-cost way to meet the demands at each of the distribution centers.

Dallas needs to receive 800 air-conditioners per month, Atlanta needs 600, and Denver needs 200. Houston has 750 air-conditioners available each month, Phoenix has 550, and Memphis has 300.

The shipping cost per unit from Houston to Dallas is $8, to Atlanta is $12, and to Denver is $10. Due to truck capacity limits, no more than 50 air-conditioners can be shipped between Houston and Denver each month.

The cost per unit from Phoenix to Dallas is $10, and to Denver is $9. Air conditioners from Phoenix are never shipped to Atlanta.

The cost per unit from Memphis to Dallas is $11, to Atlanta is $8, and to Denver is $12.

Formulate a linear optimization model to determine how many units should be shipped from each plant to each regional distribution center. You do not need to solve the problem.

4. Arnoff Enterprises manufactures the CPU for a line of computers. The CPUs are manufactured in Seattle and Santa Clara and shipped to warehouses in Pittsburgh, Mobile, Denver, Los Angeles, and Washington, D.C. The following table shows the number of CPUs available at each plant, the number of CPUs required by each warehouse, and the shipping costs (in dollars per CPU).

(a) Draw a network diagram of the problem.

(b) Are supply and demand equal to each other? No

(c) Formulate a linear optimization model to determine the distribution plan that will minimize cost while meeting as much demand as possible.

Since supply is less than demand, we will need to include a dummy origin in our formulation with a capacity of 4000 CPUs.

(d) Enter the model in Excel. Please turn in your spreadsheet.

(e) Report the optimal solution and its cost.

(f) Which, if any, warehouses will have shortages and how big will the shortages be?

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