9514 1404 393
9514 1404 393
Answer:
a) P = -28(x -112)² +7500
b) $102.55 or $121.45
Step-by-step explanation:
a) A quadratic relation with a maximum of 7500 at x=112 can be written in vertex form as ...
P = a(x -112)² +7500
The other given point (x, P) = (89, -7312) can be used to find the value of 'a'.
-7312 = a(89 -112)² +7500
-14812 = a(529)
a = -14812/529 = -28
So, the desired quadratic relation is ...
P = -28(x -112)² +7500
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b) The values of x that make P = 5000 can be found from ...
5000 = -28(x -112)² +7500
-2500 = -28(x -112)² . . . . . . . . subtract 7500
89.286 = (x -112)² . . . . . . . . . . . divide by -28
±9.45 = x -112 . . . . . . . . . . take the square root
x = 112 ± 9.45 = {102.55, 121.45}
Setting the price at about $102.55, or $121.45, will yield a profit of $5000.
