Answer to Question #180030 in Calculus for Billy

Question

 Duke’s Lunch Buffet currently sells 2500 lunches per week at a price of $11 per meal. They estimate that for each $1 increase in price, they will lose 150 customers per week. At what price should Duke’s sell their lunches to maximize their weekly revenue?

Answer 1

Solution

Increasing price on x the number of customers per week is N(x) = 2500-150x.

Price is P(x) = 11+x

Weekly revenue is

R(x) = N(x)*P(x) = (2500-150x)*(x+11)

Condition of extremum

R’(x) = -150(x+11)+ (2500-150x) = -300x+850 = 0 => x = 850/300 = 2.83

Let’s check R”(x) = -300 <0 => x = 2.83 is a point of maximum.

Therefore the price to maximize weekly revenue is P(2.83) = 13.83

Answer

Price to maximize weekly revenue is $13.83