Question

Exhibit A

Davidson Electronics manufactures two LCD television monitors, identified as Model A and Model B. Each model has its lowest possible production cost when produced on Davidson’s new production line. However, the new production line does not have the capacity to handle the total production of both models. As a result, at least some of the production must be routed to a higher-cost, old production line. The following table shows the minimum production requirements for next month, the production line capacities in units per month, and the production cost per unit for each production line.

For contractual employment issues, the number of Model A units produced on the Old Line must be at least 10% of all units produced during the month on both production lines.

You must use the information provided to formulate a linear programming model to minimize cost of production. You will use four decision variables in your formulation, each representing number of units of each model produced on each of the lines: AN (model A, New line), AO (model A, Old line), BN (model B, New line), BO (model B, Old line)

	Production Cost per Line		Min. Production Requirement
Model	New Line (N)	Old Line (O)
A	$30	$50	50,000
B	$25	$40	70,000
Line Capacity	80,000	60,000

1. Use the information in Exhibit A. Which of the following sets the minimum production limit for Model B?

A.		BN + BO < 70,000
B.		BN + BO > 70,000
C.		25BN + 40BO < 70,000
D.		25BN + 40BO > 70,000

2. Use the information in Exhibit A. Which of the following is the constraint which ensures the number of Model A units produced on the Old Line is at least 10% of all units produced?

A.		AN + AO + BN + BO > 0.1
B.		-3AN +45AO -2.5BN -4BO > 0
C.		AN > 0.1
D.		-0.1AN + 0.9AO -0.1BN -0.1BO > 0

Answer 1

The decision variables are as follows-

AN (Number of units of model A produced on New line),

AO (Number of units of model A produced on Old line),

BN (Number of units of model B produced on New line),

BO (Number of units of model B produced on Old line)

Ans 1)

The minimum production requirement of Model B = 70,000

Thus the combined number of units of Model B that are produced on both the new and old line must be greater than or equal to 70,000, i.e.

BO + BN >= 70,000

Hence the correct answer is the option B.

Ans 2)

The number of Model A units produced on the Old Line must be at least 10% of all units produced during the month on both production lines, i.e.

AO >= 10% of (AO + AN + BO + BN)

AO >= 0.10 * (AO + AN + BO + BN)

AO >= 0.10AO + 0.10AN + 0.10BO + 0.10BN

AO - 0.10AO - 0.10AN - 0.10BO - 0.10BN >= 0

0.9AO - 0.1AN - 0.10BO - 0.10BN >= 0

Hence the correct answer is option D.