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July 29, 2014

July 29, 2014

Posted by **uma** on Wednesday, June 6, 2012 at 3:39am.

Resource Requirements

Cost/Unit Labor Hours/Unit

Clock $7 2

Radio 10 3

Toaster 5 2

The manufacturer has a daily production budget of $2,000 and maximum of 660 hours of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios for $20, and toasters for $12.The company wants to know the optimal product mix that will maximize profit.

a) Formulate a linear programming model for this problem;

b) Solve the model by using the computer.

- linear programming -
**MathMate**, Wednesday, June 6, 2012 at 12:58pmGiven:

Cost/Unit Labor Hours/Unit

Clock $7 2

Radio 10 3

Toaster 5 2

Implicitly, all quantities produced daily are to be positive, so

=>

c ≥ 0

r ≥ 0

t ≥ 0

The manufacturer has a daily production budget of $2,000

=>

7c+10r+5t ≤ 2000

and maximum of 660 hours of labor.

=>

2c+3r+2t ≤ 660

Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters.

=>

c ≤ 200

r ≤ 300

t ≤ 150

Clocks sell for $15, radios for $20, and toasters for $12.The company wants to know the optimal product mix that will maximize profit.

=>

profit for clocks = 15-7 = 8

profit for radios = 20-10 = 10

profit for toasters = 12-5 = 7

Also, labour cost is not provided, so the 600 hours will be assumed a fixed cost.

=>

Z=8c+10r+7t (objective function)

Feed in all these inequalities to your linear programming solver.

I get c=178, r=0, t=150

for Z=2474, 656 hours, and cost = $1996

Check my results.

Check my

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