UWreck junkyard decides to construct a new rectangular storage yard with one sid

Question

UWreck junkyard decides to construct a new rectangular storage yard with one side adjacent to a current storage area that is already fenced. Another side of the new yard is next to a highway. The fencing for the side next to the highway costs $30 per foot and the other two sides cost $12 per foot. A 6-foot wide gate that costs $250 will be put in the side that is next to the highway. If $5500 is budgeted for the new storage yard and the given prices include labor and tax, what dimensions create the largest storage yard? Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7

Explanation / Answer

Total Budget : $5500

step 1 : Remove gate cost i.e. $250 for 6 foot

step 2 : Remaining budget : 5500-250 = $5250

Step 3: Let Length of side next to highway is X foot and other side is Y

Step 4: Total Cost for fencing (for 2 other sides + highway side - gate length)

= $12(2Y) + $30(X -6)

Step 5: Total cost should be equal to budget for maximum utilization

24Y + 30X - 180 =5250

24Y + 30X = 5430

Step 6: Largest storage yard means Largest Area : XY

Area = [X* (5430- 30X)]/24

d(area)/dX = 0 (for Largest area)

5430 - 60X = 0

X =543/6 = 181/2 = 90.5 foot

Y = [5430 - 30* 90.5]/24

= [5430-2715]/24= 113.125 Foot

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