A company calculates its expected profits as a function of the quantity of the items it can sell. How much are their expected profits if the company’s profit function is P(q)=q³−2000q+500 and their current sales quantity, q, is 60? (Answer w/ solution)
Choices:
- 204 500
- 115 900
- 96 500
- 7 900
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Expected profit is 96500 if current sales quantity is 60 for profit function P(q) = q³−2000q+500
Given:
- P(q) is expected profits as a function of the quantity (q) of the items it can sell
- P(q) = q³−2000q+500
- current sales quantity, q = 60
To Find:
- Expected profits
Solution:
Step 1:
Substitute q =60 in the given expected profit function P(q) = q³−2000q+500
P(60) = (60)³−2000(60)+500
Step 2:
Solve for P:
P(60) = 216000 - 120000 + 500
=> P(60) = 96000 + 500
=> P(60) = 96500
Correct option is 96500
Expected profit is 96500 if current sales quantity is 60
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