Reference no: EM131232915
Consider a window company with only three employees which makes two different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. They earn $60 profit for each wood-framed window and $30 profit for each aluminum-framed window. Employee 1 makes the wood frames, and can make 6 per day. Employee 2 makes the aluminum frames, and can make 4 per day. Employee 3 forms and cuts the glass, and can make 48 square feet of glass per day. Each wood-framed window uses 6 square feet of glass and each aluminum-framed window uses 8 square feet of glass.
Let x1 and x2 be the number of wood-framed and aluminum-framed windows, respectively. The linear programming model can be formulated as:
maximize 60x1 + 30x2
subject to
6x1 + 8x2 ≤ 48
x1 ≤ 6
x2 ≤ 4
x1,x2 ≥0
The optimal solution to this problem is (x1, x2) = (6, 1.5), with an optimal cost of 405.
(a) Suppose that one day, Employee 1 offers to work overtime to produce up to 9 wood frames instead of 6, but asks that he be paid an extra fixed amount of $90. Can his offer be evaluated without re-solving the model? Explain why or why not.
(b) Suppose that on a different day, Employee 1 offers to work overtime to produce up to 7 wood frames instead of 6, but asks that he be paid an extra fixed amount of $30. Is this a good deal from the company’s point of view?
(c) What would be the change in total profit if the company agreed to Employee 1’s offer from part b)?
(d) Suppose that now Employee 2 offers to work overtime to produce up to 6 wood frames instead of 4, but asks that he be paid an extra fixed amount of $1. Is this a good deal from the company’s point of view?
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