Need help with word problems that use quadratic functions….please?
Am I right???
1)Mr. Cassidy owns a farm that has land adjacent to river where he wants to make a pasture for his cattle. He has 312 yards of wire that he will electrify to enclose the three sides of the pasture, and he will use the riverbank as the fourth side. What should the dimensions of the pasture be if he wants the maximum area? What is the area?
For this one I got- Width= 156, Length= 156, and the maximum area is A(x) = 24,336 sq. yards
2)The profit function for the Haggard Apple Orchard’s out-of-state sales is P(x) = -x^2 + 276 – 11,454, where x is the number of pounds of apples in hundreds and P(x) is the profit in dollars. How many pounds should be sold out of state to produce a maximum profit, and what is that profit?
For this one I got- 1,350 pound should be sold, and the maximum profit is $11,271.75
Thanks for your help. =)
1) wire = 312 yards
let x = sides ending the river
312 – 2x = side opposite the river
A = x(312 – 2x)= 312 x – 2x^2
A’ = 312 – 4x = 0
4x = 312
x = 78
312 – 2x = 156
A = 78(156) = 12168
2) P(x) = -x^2 + 276 – 11454= -x^2 -11178
This problem looks inaccurate since any value for x will yield a loss and not profit.
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