Management Science

Part 1

1- A studio purchases photographs and art prints, frames them then sells then in the studio. It costs the studio $20 to purchase each photographs and it takes 2 hours to frame it. It costs $25 to purchase each art print and takes 5 hours to frames it. The studio has at most $400 to spend and at most 60 hours to frame. It makes $30 profit on each photograph and $50 profit on each art print. Find the number of photographs and art prints that the studio should purchase to maximize stores profit.
Required:
Write the complete linear programming model for this problem. List the decision objective function and all constraints.

2- London Drugs needs to decide how many pharmacists and technician are needed to run all its pharmacies. London Drugs managers must meet all three constraints (listed below) while minimizing labour cost. Use the management scientist output on the following page to answer the questions below:
Note: pharmacist is denoted with (P) and technicians with (T).

The objective function Coefficients represent the labour cost per hour for P and T.
Constraint 1 is ‘prescription load forecast.
Constraint 2 is ‘ratio of pharmacist to technician requirements.
Constraint 3 is ’minimum number of pharmacists.

A)    New rules allow technicians to do some of the work of pharmacists. As a result, management has decided to change the hourly rate pay for both pharmacists and technicians. Going forward, the hourly rate of pay for technicians will be $25 while th hourly rate for pharmacists will be $35.

Do we need to re-solve the LP problem?

What is the revised objective function value?

B)    If the wage of pharmacists increases by $1.5 and prescription load forecast drops by 10, do we need to re-solve the LP problem?

What does the dual price of constraint 1 indicate? Explain.
In constrain 2 binding? Explain.

3- Due to increase competition, Jared King owner of King Oil, is considering purchasing more equipment for his business. His alternatives are shown in the following table with the corresponding profit figures:
Equipment Options    Favorable market    Unfavorable market
SMC    250,000    -100,000
Titan    75,000    -25,000
Festo    300,000    -200,000

A)    If Jared continues to be as optimistic as ever, what type of equipment would he purchase?
B)    Bob is the VP of finance and attributes his success to his pessimistic attitude about business and the oil industry. What type of equipment would Bob Purchase?
C)    Jared has just read an article stating that the chance of a favorable market for oil products was 60%, while the chance of an unfavorable market was only 40%. What is the optimal decision using the expected value approach? What is the expected value for the optimal decision?
D)    How much should Jared pay for a study that would give him additional information as to whether the market will be favorable or not?

4- In the past 30 days, the OC Bookstore has sold either 5,7,8 or 10 lottery tickets. The number of the days that each sales level occurred is shown in the table below:

# of ticket sold    # od days
5    9
7    10
8    7
10    4

A)    Use the relative frequency approach to construct a probability distribution and show that it satisfies the two required conditions for probability distribution.
B)    Calculate the expected number od daily lottery sold.

5- A payoff table is giving as:
S1    S2
D1    4    11
D2    9    0

A)    Using sensitivity analysis, determine the range of values of the probability of the state of nature s1 over which each of the decision alternatives has the largest expected value.
B)    Suppose P(s1) = 0.3 and P(s2) = 0.7. What is the best decision using the expected value approach (show your calculation).

6- Video Tech is considering marketing one of two new video games for the coming holiday season: Battle Pacific or space Pirates.  Battle Pacific is a unique game and appears to have no competition. Estimated profits are as follows:
Battle Pacific     Demand
High    Medium    Low
Profits (in 000’s)    $1000    $700    $300
Probability    0.2    0.5    0.3

Video Tech is optimistic about its Space Pirates game. However, the concern is the profitability will be affected by a competitor’s introduction of a similar game.
Estimate profits with and without competition are as follows:
Space Pirates
(With)     Demand
High    Medium    Low
Profits (in 000’s)    $800    $400    $200
Probability    0.3    0.4    0.3

Space Pirates
(Without)    Demand
High    Medium    Low
Profits (in 000’s)    $1600    $800    $400
Probability    0.5    0.3    0.2

A    Using the space provided on the next page, draw and fully label a decision tree.
B    For planning purpose, Video Tech management believe there is a 0.6 probability that its competitor will produce a new game similar to Space Pirates. Using expected value, determine a recommended decision for which of the two video games to bring to market. Show all calculations in the space immediately bellow.

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