INTRO TO LINEAR PROGRAMMING

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?

T-shirt & Hoodie Problem

Objective Function

The equation that determines your profit or total amount.

P = 6x + 10y x: # of t-shirtsy: # of hoodies

Constraints

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 + 10yP = 6(80) + 10(80)

Solution: 80 t-shirts and 80 hoodies

Profit = $1,280

Maximize: P = 2x + y

Constraints: