Intro to Linear Programming

T-shirt & Hoodie Problem A t-shirt company makes t-shirts and hoodies. They can make between 80 and 100 t-shirts in one day. They can produce between 50 and 80 hoodies in one day. They can make, at most, 160 total units in one day. If the profit on each t-shirt is $6 and the profit on each hoodie is $10, how many of each kind do they need to make a maximum profit? What will this maximum profit be?

Objective Function The equation that determines your profit or total amount. P = 6x + 10y x: # of t-shirts y: # of hoodies

Constraints y ≥ 0 80 ≤ x ≤100 80 ≤ y ≤100 x + y ≤ 160 Inequalities that give you the boundaries of the situation. x ≥ 0 y ≥ 0 80 ≤ x ≤100 80 ≤ y ≤100 x + y ≤ 160

Your Goal Determine the number of t-shirts and the number of hoodies that should be made in or to maximize the profit.

(80, 80) (80, 50) (100, 50) (100, 60)

Your Solution The point that will maximize the profit will be one of the vertices on the boundary (4 corners) Plug in each point until you find the largest profit.

(80, 80) (80, 50) (100, 50) (100, 60) P = 6x + 10y

P = 6x + 10y P = 6(80) + 10(80) Solution: 80 t-shirts and 80 hoodies Profit = $1,280

Maximize: P = 2x + y Constraints: