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The question is Mr.Bryant wants to add a new rectangular screened porch onto his house.The cost of the screen porch is the function of its size.

The length of the porch must be twice its width the materials cost approximately 55 dollars per square foot and labor is about $4500. Mr.Bryant can spend no more than 9,890 dollars on his screened porch.

What is the maximum length of the porch that Mr.Bryant can afford What i got from this problem is that the length of the rectangular is 2W and the width is W. and that 55ps + 4500 = 9890. i know to find the maximum i have to use an calculator but i can't even find the equation to put in first. How would i solve this?

Gerry Myerson
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MATH ASKER
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1 Answers1

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width = W

length = 2W

Area = length x width

Perimeter = 2length + 2width

Cost = 55xPerimeter + 4500

Cost <= 9890

Put them all together and what is the maximum W? Then what is the maximum area?

So you start by doing Area: length x width = 2W * W = $2W^2$. And you keep going.

fleablood
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  • How will i go on after it than....Perimeter = 2(2W) + 2(w) P=4W + 2W..than P=6W and than i plug it in the cost equation – MATH ASKER Oct 10 '15 at 22:32
  • Yes, keep going. Cost = 55*6W + 4500. – fleablood Oct 10 '15 at 22:45
  • Ohh than i just have to plug the equation in the calculator, graph it and find the maximum right? Is that how i do it? so i graph Y = 55(6X) + 4500 and see the maximum, and find the one thats less than 9890? is that correct? – MATH ASKER Oct 10 '15 at 23:02
  • how is per square foot perimeter? – MATH ASKER Oct 10 '15 at 23:04
  • Are you sure it is 55 feet per square foot or just 55 feet per foot? If it's 55 per square foot, we don't use perimeter at all. It's COST = 55*Area + 4500.

    If it's 55 feet per foot. COST = 55Perimeter + 4500.

    Either we you set that to less than or equal to 9890 to get the maximum W and figure the area accordingly.

     – fleablood Oct 10 '15 at 23:23
  • if its per square foot...but how would i know when to use area or perimeter...I have a test on monday and if i could know how to do that it would help me a lot. Would you be able to help me how to do it? – – MATH ASKER Oct 11 '15 at 00:42