Question

A carpenter sells desks for $30 each and, at this price, sells 100 desks per month. The carpenter estimates that for each $5 increase in price, she sells 10 fewer desks per month. If the desks are manufactured at a cost of $2 per desk, at what price should they be sold to generate the greatest possible profit?

Answer 1

$47

Explanation:

Selling price of desk = p, $30

Cost price of desk = c, $ 2

Number of desk sold = d , 100

Profit (π₁) = d (p-c) ------------------------------- (1)

π₂ = (d-10) [(p+5)-c]-----------------------(2)

At greatest profit Δ π = 0

(d-10) [(p+5)-c] - [d (p-c) ] =0------------------------------- (3)

Substituting into (3)

(100-10)[p+5- 2] - [100(p-2)] =0

90 [p+5-2]- [100p-200] =0

90p +450-180-100p+ 200=0

90p- 100p = -450+ 180-200

-10p = -470

p= $47

To make the greastest possible profit, the carpenter should sell each desk for $47