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4. Answer the following questions based on the information below: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 paintHan's budget is $65. Plywood costs $0.70 per square foot, planks of wood cost $0.10 per foot, andpaint costs $8 per quart.4a. What are your variables for this situation ?Your answer4b. Write inequalities to represent the material constraints.30Your answer4c. Write inequalities to represent the cost constraints."

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4a. In this case, we have 3 variables: the amount of plywood for surfaces, wood planks, and paint. Let's write some inequalities that will represent the constraints.

4b.


\begin{gathered} a\leq60ft^2 \\ b\leq36ft \\ 1qtWhere a := plywood [ft^2] ; b:=wood planks [ft] ; c = paint [qt].<p></p><p>4c. In order to get the inequalities of the cost one must apply the instructions of the sentence. For example, since every plywood costs $0.70 per square foot, one should write it as A = 0.7 x a (where A is the cost of the plywood amount). Therefore, we write the following:</p>[tex]X=(0.7\cdot a)+(0.1\cdot b)+(8\cdot c)\begin{cases}X=\cos t \\ a=\text{plywood} \\ b=\text{planks} \\ c=\text{paint}\end{cases}

There is also the constraint of the cost, "Han's budget is $65", then the cost should be less than 65. One should write the following expression:


65\ge(0.7\cdot a)+(0.1\cdot b)+(8\cdot c)

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