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In: Operations Management

(High-tech production problem) Quitmeyer Electronics Incorporated manufactures the following three microcomputer peripheral devices: internal modems, external...

(High-tech production problem) Quitmeyer Electronics Incorporated manufactures the following three microcomputer peripheral devices: internal modems, external modems, and graphics circuit boards. Each of these technical products requires time, in minutes, on two types of electronic testing equipment, as shown in the table below.

	Internal Modem	External Modem	Circuit Board
Test Device 1	7	3	12
Test Device 2	2	5	3

The first device is available 120 hours per week. The device 2 requires more preventive maintenance and may be used only 100 hours each week. The market for all three computer components is vast, and Quitmeyer Electronics believes that it can sell as many units of each product as it can manufacture. The table that follows summarizes the revenues and material costs for each product:

Device	Revenue per Unit Sold ($)	Material Cost per Unit ($)
Internal Modem	200	35
External Modem	120	25
Graphics Circuit Board	180	40

In addition, variable labor costs are $10 per hour for test device 1 and $15 per hour for test device 2. Quitmeyer Electronics wants to maximize its profits. Please define variables and set up the objective function and constraints of this problem using LP. (5 points)

Expert Solution

Let the no. of Internal Modems manufactured be Xim, external modems be Xem and Circuit board be Xcb

Total hours for Test Device 1 = (7*Xim + 3*Xem + 12*Xcb) / 60

Total Cost for Test Device 1 = ((7*Xim + 3*Xem + 12*Xcb) / 60) * 10 = (70*Xim + 30*Xem + 120*Xcb) / 60

Total hours for Test Device 2 = (2*Xim + 5*Xem + 3*Xcb) / 60

Total Cost for Test Device 2 = ((2*Xim + 5*Xem + 3*Xcb) / 60) * 15 = (30*Xim + 75*Xem + 45*Xcb) / 60

Total Labor cost = (70*Xim + 30*Xem + 120*Xcb) / 60 + (30*Xim + 75*Xem + 45*Xcb) / 60

Total Revenue = 200*Xim + 120*Xem + 180*Xcb

Total Material Cost = 35*Xim + 25*Xem + 40*Xcb

Total Profit = Total Revenue - (Total Material Cost + Total Labor cost) = 200*Xim + 120*Xem + 180*Xcb - (35*Xim + 25*Xem + 40*Xcb) + (70*Xim + 30*Xem + 120*Xcb) / 60 + (30*Xim + 75*Xem + 45*Xcb) / 60)

Total Profit = (165*Xim + 95*Xem + 140*Xcb) - (100*Xim + 105*Xem + 165*Xcb) / 60 = 163.33*Xim + 93.25*Xem + 137.25*Xcb

We have to maximize this profit

Subject to constraints:

(7*Xim + 3*Xem + 12*Xcb) / 60 <= 120...........Constraints for hours available for Test Device 1

Hence, 7*Xim + 3*Xem + 12*Xcb <= 7200

(2*Xim + 5*Xem + 3*Xcb) / 60 <= 100.............Constraints for hours available for Test Device 2

2*Xim + 5*Xem + 3*Xcb <= 6000

Xim, Xem, Xcb >= 0

Based on above, we get the formulation as:

Decision Variables = Xim, Xem, Xcb

Objective = Maximize 163.33*Xim + 93.25*Xem + 137.25*Xcb

Subject to Contraints

7*Xim + 3*Xem + 12*Xcb <= 7200

2*Xim + 5*Xem + 3*Xcb <= 6000

Xim, Xem, Xcb >= 0

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keosha answered 1 year ago

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