The Whitt Window Company, a company with only three employees, makes two different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. The company earns $300 profit for each wood-framed window and $150 profit for each aluminum-framed window. Doug makes the wood frames and can make 6 per day. Linda makes the aluminum frames and can make 4 per day. Bob 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. The company wishes to determine how many windows of each type to produce per day to maximize total profit.

Which one of the following is the correct Linear Program for this problem?

Let [tex]W[/tex] = number of wood-framed windows, and [tex]A[/tex] = number of aluminum-framed windows.

Maximize:
\[300W + 150A\]

Subject to:
\[6W + 8A \leq 48\]
\[W \leq 6\]
\[A \leq 4\]
\[W, A \geq 0\]

The Linear Program max300W+150A, subject to W+A≤48, W≤6, best represents the Whitt Window Company's problem of determining the optimal number of wood-framed and aluminum-framed windows to produce daily to maximize profit.

Explanation:

The correct Linear Program for the problem regarding the Whitt Window Company, given the constraints provided, is the second option. This option is max300W+150A, subject to W+A≤48, W≤6. The decision variables are the number of wood-framed windows (W) and the number of aluminum-framed windows (A). The Linear Program aims to maximize the total profit, which is $300 per wood-framed window and $150 per aluminum-framed window. Constraint W+A≤48 ensures that the total number of windows does not exceed the total amount of glass that can be made per day by Bob, as each window requires 6 or 8 square feet of glass respectively. Constraint W≤6 corresponds to the maximum number of wood frames that Doug can make per day.

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