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MGMT 203 Homework 4 Questions

MGMT 203 Homework 4 Questions

1. Consider the following decision table, in which the consequences are monetary payoffs.

Payoffs ($)

State of Natures

State 1

State 2

State 3

Alternative 1

100

110

120

Alternative 2

90

100

120

Alternative 3

100

110

100

Probabilities

¼

½

¼

Using the decision tree analysis, determine which alternative should decision maker choose? (25 points)

// Please draw decision tree, then calculate expected values, and finally make a conclusion based on expected values.

// You should construct decision tree and corresponding calculations on paper manually, then please scan it to send it to us.

// There is no grading for this question without any calculation and conclusion, so be careful about these things.

1. A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has constructed to illustrate this situation:

Good

Fair

Poor

Probability

0.2

0.3

0.5

Fund A

$10K

$2K

–$5K

Fund B

$6K

$4K

0

1. Draw the decision tree to represent this situation. Which fund should a decision maker choose? (25 points)

// The same rules, as mentioned at previous question, are valid for this question, too.

1. M&D Chemicals produces two produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demand for the coming month, M&D’s management specified that the combined production for products A and B must total at least 350 gallons. Separately, a major customer’s order for 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon, and product B requires 1 hours of processing time per gallon. For the coming month, 600 hours of processing time are available. M&D’s objective is to satisfy these requirements at a minimum total production cost. Production costs are $2 per gallon for product A and $3 gallon for product B.

To find the minimum-cost production schedule, formulate the M&D Chemicals problem as a linear program.

(i) Based on the solver report for this question, write total profit, the amounts of Product A and Product B. (15 points)

(ii) Based on the solver report evaluate constraints status whether binding or nonbinding. (10 points)

(iii) Based on the sensitivity report explain the meaning of shadow prices of constraints and reduced costs of variables. (15 points) This is the question for extra points.

1. Jack produces toy soldiers and trains. The selling prices are $27 for a toy soldier and $21 for a toy train. In order to produce a toy soldier, the cost of raw material and labor are $10 and $14 respectively. On the other hand, for production of a toy train, the cost of raw material and labor are $9 and $10 respectively. For each soldier, Jack spend 2 hours for polishing, and 1 hour for carpentry. For each train, he spends 1 hour for polishing, and 1 hour for carpentry. The available amount of raw material is unlimited, but considering that Jack, who can use polishing up to 100 hours in a week and 80 hours for polishing in a week. Additionally, he can sell maximum 40 toy soldiers in a week.

(i) Based on information for this question, construct linear programming model writing objective function and constraints manually. (20 points)

 

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