The Problem

Kidzone is a child-care centre. The owner, Mrs. Cuddles, would like to build a playground around the building as shown below. She has a budget of $15,000 to purchase the chain-link fence she would use to enclose the playground. Chain-link fencing is on sale for $200 for every 8ft. Determine the maximum area for this playground using the diagram and questions below

I can use excel to help me but I don't know how to do this quesiton.

1. Determine the amount of fencing, in feet, Mrs. Cuddles can purchase within her budget.

1. What is the relationship between length (l) and the two equal portions next to the building,x? What is this as an equation expressing l in terms ofx.

1. Express the perimeter of the playground (i.e. the amount of fencing) in terms ofx,wandl.

1. Now, express the perimeter of the playground (i.e. the amount of fencing) in terms ofx, andwonly, using your answers from #2 and #3 above.

1. What is the formula used to calculate area of the playground?

1. Rearrange your equation from #4 to isolatex.

1. How do you create a table of values for width,xand area (using the formulas from #5 and #6) to model this situation and then provide a graph of your results.

1. Determine the maximum area.

1. What are the dimensions (length and width) that will provide the maximum area?

1. Mrs. Cuddles would like to install special protective rubber padding on the playground that will protect the children. How much should she budget for, if the rubber padding sells for $5.75/m²?

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