Question

(PLEASE SHOW EXCEL STEPS)A manufacurer of bathroom fixtures produces fiberglass bathtubs in an assebly operations consisting of three processes: moldinig, smoothing, and painting. The number of units that can be put throught each process in an hour is shown below. (Note: the three processes are contious ans sequential; thus, no more units can be smoothed or painted than have been molded.) The labor cost Each bathtub requires 90 pounds of fiberglass, and the company has a total of 10,000 pounds of fiberglass available each week Each bathtub earns a profit of $175. The manager of the company wants to know how many hours per week to run each process in order to maximize profit. Formulate and solve a linear programing model for this problem

Process, Output, and Cost as Follows--- (Modeling: 7units/hr @ $8/hr) (Smoothing: 12units/hr @ $5/hr) (Painting: 10units/hr @ $6.50/hr)

Answer 1

Formulate LP model as below:

Let M, S, P be the number of hours to run each of the three processes - Molding (M), Smoothing (S), Painting (P) respectively.

Max 175*7M - 8M - 5S - 6.5P

s.t.

7M = 12S or, 7M - 12S = 0 number of batchtubs smoothed is equal to number of batchtubs molded

7M = 10P or, 7M - 10P = 0   number of batchtubs painted is equal to number of batchtubs molded

90*7M <= 10000

M, S, P >= 0

Solution of LP model using LINDO is as follows:

Optimal solution:

M = 15.87

S = 9.26

P = 11.11

Total profit = $ 19,198.94