Hannah B.

# Phil owns a small business that makes playground sets and playhouses. Use linear programming to decide how many of each product the company should make each day

Phil owns a small business that makes playground sets and playhouses. The production process breaks down into the prep stage, where lumber is cut and drilled, and the assembly stage. For each playground set, it takes a worker 2 hours to cut and drill the lumber and another worker 1 hour to assemble the unit. For each playhouse, it’s 1 hour for cutting and drilling and an hour and a half for assembly. Workers never work more than an 8-hour day. Phil makes $100 profit on each playground set sold and$75 profit on every playhouse sold. Use linear programming to decide how many of each product the company should make each day in order to maximize profit.
1. Write an objective function.
2. Write the constraints. (Don't forget the implied ones.)
3. Graph the constraints and shade the "region of feasible solutions."
4. Find the vertices.
5. Test the vertices in the objective function. Answer the question: how many of each product the company should make each day in order to maximize profit? What is the maximum profit?

## 1 Expert Answer

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Ismael A. answered • 11/11/16

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