if demand function is p=√9-x. find at the level of output x, the total revenue will be maximum. also find TR
Answers
We have to find the maximum of the function:
\displaystyle TC = Q^3-10Q^2 + 85Q + 10 = (12.5 - 0.125P)^3 - 10(12.5-0.125P)^2 + 85(12.5 - 0.125P) + 10TC=Q
3
−10Q
2
+85Q+10=(12.5−0.125P)
3
−10(12.5−0.125P)
2
+85(12.5−0.125P)+10
the derivative is \displaystyle 3(12.5 - 0.125P)^2*(-0.125) - 20(12.5 - 0.125P) + 853(12.5−0.125P)
2
∗(−0.125)−20(12.5−0.125P)+85
Solve it and write the roots:
\displaystyle 3(12.5 - 0.125P)^2*(-0.125) - 20(12.5-0.125P) + 85 = 03(12.5−0.125P)
2
∗(−0.125)−20(12.5−0.125P)+85=0
There is a nice tool here for loving quadratic equations:
We have to find the maximum of the function:
\displaystyle TC = Q^3-10Q^2 + 85Q + 10 = (12.5 - 0.125P)^3 - 10(12.5-0.125P)^2 + 85(12.5 - 0.125P) + 10TC=Q
3
−10Q
2
+85Q+10=(12.5−0.125P)
3
−10(12.5−0.125P)
2
+85(12.5−0.125P)+10
the derivative is \displaystyle 3(12.5 - 0.125P)^2*(-0.125) - 20(12.5 - 0.125P) + 853(12.5−0.125P)
2
∗(−0.125)−20(12.5−0.125P)+85
Solve it and write the roots:
\displaystyle 3(12.5 - 0.125P)^2*(-0.125) - 20(12.5-0.125P) + 85 = 03(12.5−0.125P)
2
∗(−0.125)−20(12.5−0.125P)+85=0
There is a nice tool here for loving quadratic equation (
Answer:
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