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
Respond to this Question
Similar Questions

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 … 
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 … 
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? 
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 … 
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 … 
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)=20x350 … 
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 … 
business
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 $7 2 Radio 10 3 Toaster 5 2 The manufacturer … 
math
A company makes two products , namely X and Y. Each product must be processed in 3 stages; welding , assembly and painting. Each unit X takes 2 hours in welding, assembling 3 hours and 1 hour in painting. Each unit Y takes 3 hours … 
Algebra
you are the manager of a firm that produces two products X and Y at zero cost. there are three types of consumers(1000 of each type) with the following valuations of the two products. consumer type Product X($) ProductY($) 1 90 60 …