linear programming

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 constrains and the objective function

Answer 1

Objective function is to maximize income.

The linear equation of the objective function is max (x1 + x2); where x1 = # of haircuts and x2 = # of haircut & color.

Constraints:

#1) 0.5*x1 + 2* x2 < =10.

0.5* x1 represents 0.5 hrs. per haircut and 2*x2 represents 2 hrs. per haircut & color.

The expression < = 10 represents that there are no more than 10 hour per day which Natalie will work.

#2) x1 + x2 < = 8

This expression represents the fact that Natalie doesn’t want more than 8 clients per day.

Recall x1 represents # of haircuts and x2 represents # of haircut & color, so x1 + x2 <=8 should make sense.