How to solve this assignment? When John decided to renovate his garage, he also

Question

How to solve this assignment?

When John decided to renovate his garage, he also wanted to attach it to his house, he also wanted to attach it to hos house. The only wall that was available to achieve this was the kitchen wall. The contractor informed him that the area of his new garage will be limited by the cost of the ;aterials he should buy. After some calculations, they decided that he could afford three walls with a total length of 68 feet. The kitchen wall would serve as the fourth wall

but john had two bigs cars, so he wanted to build a garage with the biggest possible area under his contractor's constraints.

What is the formula for the area of the garage?

Choose two dimensions to p;lug into your formula.

What areas result? If you get a negative area, your dimension was too lqrge, so select another.

Next, use the vertex formula to find the dimension that produces the maximum area of the garage. Finaly, find the maximum area.

will the garage be large enought to accommodate two cars? How does the of the kitchen wall affect the structure of the garage? Summarize your findings in writing using proper style and grammar

Explanation / Answer

Let x represent the garage width Let y represent the garage length Since once length of the garage is the kitchen wall, our entire built wall will be two widths and one length 2x+y=68 y=68-2x The area is reprsented by width times length x*y=Area =x*(68-2x)=68x-2*x^2 Graphing this as y=68x-2*x^2 yields a peak at x=17 which makes y=34 and the maximum area becomes 17*34=578 square feet, more than sufficient for two cars of width and length of 17 feet :)

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