The revenue from selling q items is R(q)=175q−q2, and the total cost is C(q)=100+6q.?
Write a function that gives the total profit earned, and find the quantity which maximizes the profit.
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Write a function that gives the total profit earned, and find the quantity which maximizes the profit.
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(I assumed q2 = q^2)
Profit = revenue - cost
= R(q) - C(q)
= 175q −q^2 -100 -6q
= −q^2 + 169q - 100
To maximize profit, take the first derivative w.r.t. q, this must equal zero.
dprofit/dq = -2q + 169 = 0
Now solve for q
q* = 169/2