Linear programming algebra 2

Question

Natalie is a hair stylist when making appointments for her clients she allots 30 minutes for each cut and 2 hours for each cut and color she has 10 hours available for appointments each day and prefers to see no more than 8 clients each cut costs 40 and each cut and color costs 100 how many of each type of appointment should she schedule each day to maximize income

Please define profit equation.

Answer 1

x + y = 8

x/2 +2y = 10

x = cut clients, y = cut&color clients

40x + 100y = daily profit

P(x,y) = 40x +100y

P(x) =40x +100(5-x/4) =15x +500

P(4) = 60+500 = 560

P(0) = 500

what x and y values maximize R?

x y R

0 5 5(100)=500

4 4 4(40)+400 = 560

schedule 4 cut and 4 cut&color customers maximizes profit = $560

4(1/2) +4(2) = 10 hours

4+4 = 8