linear programming
posted by uma .
The Pyrotec Company produces three electrical productsclocks, radios and toasters. These products have the following resources 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 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.

Given:
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 = 157 = 8
profit for radios = 2010 = 10
profit for toasters = 125 = 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 
27523