3-4. A Production Problem. Wood Walker owns a small furniture shop. He makes thr

Question

3-4. A Production Problem. Wood Walker owns a small furniture shop. He makes three different styles of tables: A, B, C. Each table requires a certain amount of time for cutting component parts, for assembling, and for painting. Wood can sell all the units he makes. Furthermore, model C may be sold without painting. Wood employs several individuals who work on a part-time basis, so the time available for each of these activities varies from week to week. Use the data below to formulate an LP model that will help Wood determine the product mix that will maximize his profit next week. CUTTING ASSEMBLING PAINTING PROFIT PER MODEL (hrs) (hrs) (hrs) TABLE ($) 25 20 50 30 4 4 4 4 0 Unpainted C Capacity 150 200 300

Explanation / Answer

Decision variables:

Let A = No of units of A

B = No of units of B

C = No of units of C

D = No of units of Unpainted C

Objective function is to maximize profits

Max Z = 25A + 20B + 50C + 30D

Constraints:

3A + 1B + 4C + 4D <= 150(Cutting hours)

4A + 2B+ 5C + 5D <= 200(Assembling hours)

5A + 5B + 4C +0D <= 300 (Painting hours)

A,B,C,D>= 0 (Non negative constraints)

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