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Linear Programming

The Dub-Dub and Dub Company produces and markets three lines of WEB page designs: A, B, and C; A is a standard WEB page design and B and C are professional WEB page designs. The manufacturing process for the WEB page designs is such that two development operations are required - all WEB page designs pass through both operations. Each WEB page design requires 3 hours of development time in Operation 1. In Operation 2 WEB page design A requires 2 hours of development time; WEB page design B requires 4 hours; and WEB page design C requires 5 hours. Operation 1 has 50 hours of development time per week and Operation 2 has sufficient manpower to support 80 hours of development per week. The market group for Dub-Dub and Dub has projected that the demand for the standard WEB page design will be no more than 25 per week. Because WEB page designs B and C are similar in quality, the combined demand for those WEB page designs has been forecast - the total demand is ten or more, but not more than 30 per week. The sale of WEB page design A results in $7 profit while WEB page design B and C provide $8 and $8.5 profits respectively. How many of WEB page designs A, B, and C should be produced weekly if the company seeks to maximize profits? Formulate the problem as a standard LP model.

See attachment
a. Graph the problem.
b. What is the optimal solution?
c. What would the solution be if the third constraint were removed from the problem?


Solution Preview

1. Solution. Assume that we should produce WEB page designs A x pages, B y pages, and C z pages weekly. Then the profit function is
c(x,y,z)=7x+8y+8.5z (1)
We formulate this problem as the following Linear ...

Solution Summary

The solution answers the question(s) below.