Linear programming algebra 2

Question

A store sells two types of toys, A and B. The store owner pays $5 and $15 for each one unit of toy A and B respectively. One unit of toys A yields a profit of $2 while a unit of toys B yields a profit of $3. The store owner estimates that no more than 2000 toys will be sold every month and he does not plan to invest more than $18,000 in inventory of these toys. How many units of each type of toys should be stocked in order to maximize his monthly total profit?

Answer 1

Well if x, y are the units of each type sold

x, y >=0

5x + 15 y <= 18000 (cost of inventory)

x + y <= 2000

We need to maximise 2x + 3y

So

On Desmos draw the lines x=0, y=0, 5x+15y = 18000, x+y = 2000.

The shape enclosed by these four lines will have 4 vertices

At each vertex evaluate the profit function 2x + 3y. Choose the vertex with the highest profit value.

The coordinates of that vertex (x,y) will be your solution