3 questions operation research $10

1. The Charm City Inc. must select among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns,the capital requirements, and the available capital funds over the next three years are given below:

Net Present     Capital Requirements ($)

Alternative                                 Value ($)      Year 1    Year 2   Year 3

_____________________________________________________________

Warehouse expansion                 30,850          32,000               12,000     38,000

Test market new product            92,300          58,000               41,000     45,000

Advertising campaign                 40,000          25,000               12,500     11,800

Research & Development           82,000          53,000  13,000     44,000

Purchase new equipment            33,000          12,500                 4,500       8,900

_____________________________________________________________

Capital funds available                                                110,500             65,000               88,750

The company wants to select at least 3 alternatives. In addition, the company also wants to select at least two alternatives from the warehouse expansion, research & development and purchase new equipment alternatives.

Develop a capital budgeting problem to maximize the total net present value in this situation.

Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation.  Please do NOT solve the problem after formulating.

2. Jodi wants to lease a new car and start a part time business to give people car rides. She has contacted three automobile dealers for pricing information. Each dealer offered Jodi a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The three dealers provided the details about the monthly lease cost, the mileage allowance, and the cost for additional miles.

Jodi is not sure how many miles she will drive over the next three years for this business but she believes it is reasonable to assume that she will drive 10,000 miles per year, 14,000 miles per year, or 18,000 miles per year. With this assumption, Jodi estimated her total profit for the three lease options. The three lease options and the associated profits for each are given below:

Dealer       10000 Miles             14000 Miles      18000 Miles          

   A                $ 7000                   $10500              $13500

   B                 $ 8500                   $11500              $11000

   C                 $10000                 $ 9500               $ 9800

Determine the optimal decision to lease the car from a dealer and the profit associated with it by using the following decision criteria.

a.Maximax

b.Maximin

c.Equal likelihood

d. Minimax regret criterion.

3. For the problem given in Question 2, the probabilities are given by P(10000 miles) = 0.5, P(14000 miles) = 0.3 and P(18000 miles) = 0.2.

a.Compute the expected value for each decision and select the best one.

b.Compute the expected regret value for each decision and select the best one.

c. Calculate and interpret the expected value of perfect information.