Algebra II word problem. Please help

Question

A baker sells loaves of bread in two different sizes: small and large. The baker has 40 kilograms of flour to work with. Small loaves require 0.4 grams of
flour and large loaves require 0.8 grams of flour. Additionally, the baker has 800 grams of yeast; each loaf requires 10 grams. If the baker makes $1.20 profit from each large loaf and $0.50 from each small loaf, and he wants to maximize his profits, how many loaves of each size should he make?

Answer 1

x = the number of small loaves of bread

y = the number of large loaves of bread

The first equation represents how many loaves of bread can you have when you are working with up to 40 grams of flour.

0.4x + 0.8y ≤ 40 (1)

The second equation represents how many loaves of bread can you have when you are working with up to 800 grams of yeast.

10x + 10y ≤ 800 (2)

The objective function represents the profit that the baker will make for all the loaves of bread.

z = 0.5x + 1.2y

One thing to note is that x and y are not negative since we can't have a negative quantity of a product.

1.) Use the Desmos Graphing Calculator to graph the two constraint equations and find the feasible regions. The four points are (0, 0), (0, 50), (80, 0), and (60, 20) from where the two lines are intersected.

2.) Test the corner points in the objective function. One of them will give us the biggest profit.

z = 0.5(0) + 1.2(0) = 0 + 0 = 0

z = 0.5(0) + 1.2(50) = 0 + 60 = 60

z = 0.5(80) + 1.2(0) = 40 + 0 = 40

z = 0.5(60) + 1.2(20) = 30 + 24 = 54

The baker should make 0 small loaves of bread and 20 large loaves of bread for a profit of $60.