How do I solve this question? Finite Math Chapter 10

Question

A store sells two types of shirts, T-shirts (T) and

long-sleeves (L). The store owner pays $8 and $14

for each type of shirt, respectively. One T-shirt sale

yields a profit of $2, while a long sleeve shirt sale

yields a profit of $3. The store owner estimates that

no more than 2000 shirts will be sold every month

and he does not plan to invest more than $20,000 in

inventory of these clothes. How many units of each

type of shirt should be stocked in order to maximize

his monthly total profit?

Answer 1

Suppose x, y units of T and L

Then x,y >= 0

x + y <= 2000 (demand)

Cost of stock = 8x + 14 y <= 20000

Profit = 2x + 3y

So on a graphing program eg Desmos

Draw x = 0

Draw y = 0

Draw x + y = 2000

Draw 8x + 14 y = 20000

The area bounded by these four lines is the feasible region

At each of the vertices of this region calculate 2x + 3y

Choose the vertex giving the largest value of (2x + 3y)

The x, y coordinates of this will be your required answer