Problem

4. Han wants to build a dog house. He makes a list of the materials needed: - At least 60 square feet of plywood for the surfaces - At least 36 feet of wood planks for the frame of the dog house - Between 1 and 2 quarts of paint Han's budget is $\$ 65$. Plywood costs $\$ 0.70$ per square foot, planks of wood cost $\$ 0.10$ per foot, and paint costs $\$ 8$ per quart. Write inequalities to represent the material constraints and cost contraints in this situation. Be sure to specify what your variables represent.

Solution

Step 1 :Define the following variables: P for the number of square feet of plywood Han buys, W for the number of feet of wood planks Han buys, and Q for the number of quarts of paint Han buys.

Step 2 :Write the material constraints as inequalities: \(P \geq 60\), \(W \geq 36\), and \(1 \leq Q \leq 2\).

Step 3 :Write the cost constraint as an inequality: \(0.70P + 0.10W + 8Q \leq 65\).

Step 4 :The inequalities representing the material constraints are \(\boxed{P \geq 60}\), \(\boxed{W \geq 36}\), and \(\boxed{1 \leq Q \leq 2}\).

Step 5 :The inequality representing the cost constraint is \(\boxed{0.70P + 0.10W + 8Q \leq 65}\).

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Source: https://solvelyapp.com/problems/Z9ciiMrM24/

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