Question

A furniture manufacturer makes two types of furniture: chairs and sofas. The production of the sofas and chairs requires three operations: carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The prfit per chair is $90 and the profit per sofa is $75. The manufacturer wants to know how many chairs and how many sofas should be produced each day to maximize the profit.

Formulate a linear programming (LP)problem you would use to find a solution.

Answer 1

Explanation:

let chairs be C and sofas be S

The objective function is

Maximize

90C+75S=P

The constraints are

carpentry

3C+2S=66------1

finishing

9C+4S=180-----2

upholstery

2C+10S=200-----3

C>0, S>0

The linear programming is

3C+2S=66

9C+4S=180

2C+10S=200