The Pyrotec Company produces three electrical products—clocks, radios, and toast

Question

The Pyrotec Company produces three electrical products—clocks, radios, and toasters. These products have the following resource requirements:

                                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 a 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.

Explanation / Answer

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

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