Question

A manufacturer produces four parts: XJ201, XM897, TR29, and BR788. The net profit per unit are $9, $12, $15, and $11 respectively. The products are each processed in the wiring and drilling departments then go to assembly. The final step in the plant is a final inspection. The time in minutes spent at each of the four departments is listed in the following table:

                        Wiring             Drilling            Assembly        Inspection

XJ201             30                    180                  120                  30

XM897           90                    60                    240                  60

TR29               90                    120                  60                    30

BR788             60                    180                  120                  30

The labor capacity in hours for each department is listed below:

                        Wiring             Drilling            Assembly        Inspection

Capacity         1500                3000                2600                1200

The company has firm contracts for 150 units of XJ201, 100 units of XM897, 300 units of TR29, and 400 units of BR788. The company cannot sell more than 180 units of XJ201. The operations manager needs to determine how many to produce of each to maximize profits.

Part A

Requirements:

Give a typed formulation with decision variables clearly defined and all constraints clearly defined. (2 pts)

Solve the formulation in solver and save the Sensitivity Report. (2 pts)

Using Sensitivity Analysis: If sales can increase the quantity of the firm contract for XM897 to 110 units, should the operations manager allow the increase? Justify your answer. (1 pt)

Using Sensitivity Analysis: A local college student offers to work in any of the four departments for a maximum of 8 hours and is willing to work for $8.00/hour. Should the operations manager hire the college student? If so, how many hours should the college student work in each department? How much will profits increase?(1 pt)

Answer 1

Let A, B, C, and D be the number of XJ201, XM897, TR29, BR788 respectively to be produced.

Objective Function:

Maximize Z = Total profit = 9A + 12B + 15C + 11D

Subject to,

30A + 90B + 90C + 60D <= 1500*60 (wiring)
180A + 60B + 120C + 180D <= 3000*60 (drilling)
120A + 240B + 60C + 120D <= 2600*60 (assembly)
30A + 60B + 30C + 30D <= 1200*60 (inspection)

A >= 150 (minimum demand of A)
B >= 100 (minimum demand of B)
C >= 300 (minimum demand of C)
D >= 400 (minimum demand of D)

A <= 180 (max demand of A)

A, B, C, >= 0

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Answer Report

Sensitivity Report

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There is a shadow price of -2.4 associated with the minimum demand constraint for B. So if demand is increased to 110, the profit will reduce to $15,828 - $2.4*10 = $15,804. So, the operations manager may not be interested in change on contract.

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Wiring has a maximum shadow price. So, this extra capacity can be employed in wiring department. Increase in profit for this extra 480 hours will be 480 x 0.153 = $73.6 and the pay rate is $64 (=8 x 8). So, the effective increase will be $9.6.