MSA 8100 – Intro To Business Analytics

Review Problem 1 (LP)

Harry & David’s Co. plans to sell three variety of gift boxes this holiday season. All gift boxes contain chocolate and fruit. The “Chocolate Lovers” box sells for $60, the “Fruit Lovers” box sells for $50, and the “Supersize Variety” box sells for $70. Each “Chocolate Lovers” gift box requires 4 pounds of chocolate and 2 pounds of fruit. Each “Fruit Lovers” box requires 2 pounds of chocolate and 3 pounds of fruit. Each “Supersize Variety” box requires 5 pounds of chocolate and 2 pound of fruit. The company has 240 pounds of chocolate and 120 pounds of fruit.

The total space available at Harry & David’s limits the amount of gift boxes to 55. Also, the company wants to produce at least twice as many “Chocolate Lovers” gift boxes as “Fruit” gift boxes.

a. Use Solver to maximize Harry & David’s revenue.

b. Use Solver Table to show how the optimal production levels of gift boxes vary as the amount of fruit increases from 120 pounds to 200 pounds (in 10 pound increments)

Review Problem 2 (LP)

The Villanova Employees Credit Union is trying to determine where its assets should be invested during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rates of return on each type of investment are known to be the following: bonds 10%, home loans 16%, auto loans 13%, and personal loans 20%. To ensure that the credit union’s portfolio is not too risky, the investment manager has placed the following three restrictions on the portfolio:

(1) the amount invested in personal loans cannot exceed the amount invested in bonds

(2) the amount invested in home loans cannot exceed the amount invested in auto loans

(3) no more than 20% of the total amount invested can be in personal loans

Use Solver to determine how to allocate the Credit Union’s available funds to maximize the annual return on its investment portfolio.

Review Problem 3 (IP)

The software support division of GE has nine projects that can be performed. Each project requires different amounts of development time and testing time. In the coming planning period 1100 hours of development time and 900 hours of testing time are available. The projected revenue and time required for each project are shown below. Which projects should be selected to maximize revenue?

Development Testing

Project                                 Time (hr)                               Time (hr)                            Revenue

1                                               80                                             67                                      $23,000

2                                             248                                           208                                    $73,000

3                                              41                                               34                                    $12,000

4                                              10                                               92                                    $32,000

5                                             240                                            202                                   $71,000

6                                             195                                             164                                   $57,000

7                                             269                                             226                                  $69,000

8                                             110                                              92                                    $32,000

9                                              94                                                78                                  $26,000

Review Problem 4 (IP)

Eastinghouse sells air conditioners. Annual demand for air conditioners in each region of the country is:

East 100k; South 150k; Midwest 110k; West 90k.

The company is considering building its air conditioners in four different cities: NY, Atlanta, Chicago, and

LA. The company has estimated the following unit production and shipping costs between plants and

regions, and annual fixed costs for the plants.

Unit production and shipping costs

From\To East South Midwest West,Annual fixed ,costs respectively

NY $206 $225 $230 $290 $6,000,000

Atlanta $225 $206 $221 $270 $5,500,000

Chicago $230 $221 $208 $262 $5,800,000

LA $290 $270 $262 $215 $6,200,000

Any factory can produce up to 150k air conditioners per year. At least 50k units of the Midwest demand

for air conditioners must come from NY, & at least 50k units of the Midwest demand must come from

Atlanta. Determine how Eastinghouse can minimize the annual cost of meeting demand for air

conditioners.

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