Acarpenter 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?

$47

Step-by-step 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

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

ask for details followreport by buttfacelily 2 minutes ago

answers

rauschg

rauschg · hand

know the answer? add it here!

step-by-step explanation: