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2 answers:
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Answer:
x = {40, 80}
Step-by-step explanation:
The profit equation is ...
P = R - C = 100x -0.5x^2 -(40x +800)
P = -0.5x^2 +60x -800
We want to find values of x such that P = 800
800 = -0.5x^2 +60x -800
1600 = -0.5x^2 +60x . . . . add 800
-3200 = x^2 -120x . . . . . . . multiply by -2
400 = x^2 -120x +3600 . . . . add 3600 to complete the square
400 = (x -60)^2 . . . . . . write as a square
±20 = x -60 . . . . . . . . . take the square root
x = 60 ± 20 = {40, 80}
The values of production level (x) that will create profit of $800 are 40 and 80 units.
