I worked out this problem using microsoft office's excel's solver application and I want to make sure I did it right.
The answer I got was 1000 for product A, 1000 for product B.
Here is the problem:
A company manufactures two products:Product A and Product B.
• Product A can be sold for $145 per unit and B for $75 per unit.
• Management requires that at least 2000 units be manufactured each month.
• Product A requires 5 hours of labor per unit, and product B requires 3 hours.
• The cost of labor is $15 per hour and a total of 8000 hours are available per month.
a)How many of each product should they manufacture each month?
Exercise 8 - Optimization Problem
Product Price Labor in Hours Labor Cost (in dollars)
A 145 5 15 Cost of Labor: 15 per hour
B 75 3 15 Total hours available: 8000
Design Variables
Product A x1 1000
Product A x2 1000
Objective Function
Cost = 145(x1) + 75(x2) 220000
Contraints
145(x1) + 5(x2) -15 => 0 149985
75(x1) + 3(x2) - 15 => 0 77985
x1 + x2 => 2000 2000
5(x1) + 3 (x2) => 8000 8000
x1=> 0 1000
x2=> 0 1000