Professor Shad 1324 Lab 3 Part A Name: 3) Use the Simplex method to solve the fo

Question

Professor Shad 1324 Lab 3 Part A Name: 3) Use the Simplex method to solve the following linear programming problem. A company manufactures outdoor furniture consisting of regular chairs, rocking c chaise lounges. Each piece of furniture passes through three different production departments: fabrication, assembly, and finishing. Each regular chair takes 1 hour 2 hours to assemble, and 3 hours to finish. Each rocking chair takes 2 hours to fabr hours to assemble, and 3 hours to finish. Each chaise lounge takes 3 hours to t hours to assemble, and 2 hours to finish. There are 2,500 fabrication d hairs, and to fabricate, icate, 2 abricate, 4 labor-hours available in the epartment, 3,000 in the assembly department, and 3,500 in the finishing he company makes a profit of $17 on each regular chair, $24 on each rocking chair, and $31 on each chaise lounge, How many chairs of each type should the company produce in order to maximize profit? What is the maximum profit? Define the variables. Be specific. Clearly state the constraints (inequalities)

Explanation / Answer

Variables

let the optimal number of chair for each is as following -

Regular chairs = C

Rocking chairs = R

Chause Lounges = L

Constraints

1. maximum labor hour avallable in fabrication dept is 2500 hours : C + 2R+3L <= 2500

2. maximum labor hour avallable in assembly dept is 3000 hours : 2C + 2R+4L <= 3000

3. maximum labor hour avallable in finishing dept is 3500 hours : 3C + 3R+2L <= 3500

Objective

maximize the profit = 17C+24R+31L

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