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.
Solve the formulation in solver and save the Sensitivity Report.
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.
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?