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    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?

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    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 ...

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