Answer to Question #176898 in Financial Math for MuhammadAslam

Question

A manufacturing plant had a capacity of 25 article per week . experience has shown that m article per week can be sold at a price of C rupees cash . where C = 165 _ 3m and a cost of producing m article is 700 + 5m + m^2 rupees. How many articles should be made cash week to get a maximum profit

Answer 1

Articles to produce to maximize profit

M articles sold at price C=165-3m; so,

$Revenue for m articles= Price\times No of articles$

$Revenue for m articles= (165-3m)\times m= 165m-3m^2$

Cost = 700+5m+m^2

To maximize profit, marginal revenue(MR)= marginal cost(MC); so,

Differentiate the two equations

MR=165-6m

MC=5+2m

165-6m=5+2m; like terms

160=8m; divide by 8 both sides

m= 20 articles