# linear programming

posted by .

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
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 -

Given:

Cost/Unit Labor Hours/Unit
Clock \$7 2
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 -

27523

## Similar Questions

1. ### Calculus 2

A manufacturer sells two products, one at a price of \$3000 a unit and the other at a price of \$12000 a unit. A quantity q1 of the first product and q2 of the second product are sold at a total cost of \$5000 to the manufacturer. Express …
2. ### calc2

A manufacturer sells two products, one at a price of \$3000 a unit and the other at a price of \$12000 a unit. A quantity q1 of the first product and q2 of the second product are sold at a total cost of \$5000 to the manufacturer. Express …
3. ### Math

Herman Company has three products in its ending inventory. Specific per unit data for each of the products are as follows: Required: What unit values should Herman use for each of its products when applying the LCM rule to ending inventory?
4. ### Math

Herman Company has three products in its ending inventory. Specific per unit data for each of the products are as follows: Product1 product2 product3 cost \$20 \$90 \$50 replacement cost 18 85 40 selling price 40 120 70 disposal costs …
5. ### linear programming

A manufacturer has a maximum of 240, 360, and 180 kilograms of wood, plastic and steel available. The company produces two products, A and B. Each unit of A requires 1, 3 and 2 kilograms of wood, plastic and steel respectively; each …
6. ### College Algebra

A manufacturer of radios estimates that his daily cost of producing x radios is given by the equation C=350+5x. The equation R=25x represents the revenue in dollars from selling x radios. *Profit function,P(x)=R(x)-C(x),P(x)=20x-350 …
7. ### Accounting

Spencer Company manufactures and sells three products. Relevant per unit data concerning each product are given below. Product A B C Selling price \$9 \$12 \$14 Variable costs and expenses \$3 \$9.50 \$12 Machine hours to produce 2 1 2 Compute …