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

The Pyrotec Company produces three electrical products-clocks, 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.

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

- linear programming -
**nia**, Monday, March 2, 2015 at 3:00pm
27523

## Answer This Question

## Related Questions

- business - The Pyrotec Company produces three electrical products-clocks, radios...
- Math - Herman Company has three products in its ending inventory. Specific per ...
- Accounting - Spencer Company manufactures and sells three products. Relevant per...
- Algebra - you are the manager of a firm that produces two products X and Y at ...
- math - A company makes two products , namely X and Y. Each product must be ...
- Math - Herman Company has three products in its ending inventory. Specific per ...
- Accounting - Cambridge Manufacturing Company, Inc. has 200 labor-hours available...
- math - Four products are processed sequentially on three machines. The following...
- Linear Programming - We produce two products: product 1 and product 2 on two ...
- College microeconomics - Need some help with these questions....Thanks in ...

More Related Questions