Problem 1A new small manufacturing company, IGEW, makes two customized computer models, the CFH Model and the XPQ Model. It is a family-run business that is not operating on a production line where many units can be made each day. IGEW firmly believes that these two products, created one at a time with specially designed machinery, will lure Generation Z* eventually into its fold, although no statistical evidence has been gathered yet to support this projection.

Considering the requisite data and formulating the problem as a linear program (LP), IGEW has developed the following program for each day.

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(P) Maximize (profit in thousands)

s.t.

(available assembly hours)

(available labor hours)

minimal production level)



where  is the number of basic CFH Models and  is the number of XPQ models designated for production during the next timeframe.

1. Graph the constraints in the space below or on the next page and use the graphical method (not the corner point method) to find the optimal solution to the LP. Indicate clearly the feasible region. Recall that the optimal solution consists of the optimum and the maximum value. At least one iso-profit or iso-cost line must be drawn. Label the equation of at least one of them on the line itself. A non-integer solution, if one exists, should be expressed in hundredths.

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(b) How many CFH Models and XPQ Models can be produced daily? What is the best profit IGEW can realize?

(c) Which constraints are binding at the optimal solution? Specify the slack or surplus for all resources. Use a Resource Utilization Table to display the results.

(d) At the optimal solution, how many assembly hours should be used? How many labor hours? By how much is the required production level surpassed, if at all?

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Problem 2 NLV Drilling Company produces a variety of specialty valves for oil field equipment. Due to increased demand caused by recent activity in the oil fields, management has decided to open a new manufacturing facility. Three locations are being considered, and the size of the facility depends on the location. The table below projects the total semi-monthly profit (in \$1,000) for each possible location given each demand possibility.

Total Monthly Profit in \$1,000s

High Medium Low

Alternatives Demand Demand Demand

Odessa, TX 140 130 30

New Orleans, LA 130 155 40

Shreveport, LA 165 150 70

Which location should be selected based on

1. the pessimistic approach?
2. the Laplace criterion?
3. the criterion of realism with coefficient of realism based on your feeling three times as pessimistic as optimistic.

(d) minimax regret?

(e) Based on your responses, what is your preferential model to use for this problem’s decision-making? Write a complete sentence (or two) as part of your report generation for upper-level management. You’ll be graded on your composition.

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Problem 3 After further consultation with the analytics personnel from NLU Drilling, it has been decided to impart probabilities of .35 for high demand, .45 for medium demand, and .20 for low demand.

(a) Draw a decision tree to assist management’s decision-making.

(b) Which location should be selected to maximize the expected profit? Why? Indicate your choice on the preceding decision tree.

(c) Find the expected value of perfect information and explain what this means.

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