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:$47Step-by-step explanation:Selling price of desk =  p, $30Cost price of desk = c,  $ 2Number of desk sold = d , 100Profit (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)] =090 [p+5-2]- [100p-200] =090p +450-180-100p+ 200=090p- 100p = -450+ 180-200-10p = -470p=   $47 To make the greastest possible profit,  the carpenter should sell each desk for $47