Mr. Thibodeau makes chocolate chip muffins and very-berry muffins to sell in his bakery. He is limited by the following constraints:

Question

• Each chocolate chip muffin requires 4 minutes mix time, and the very-berry muffins require 3 minutes mix time. The mixer is only available for 2 hours (120 minutes) each day.
• Each chocolate chip muffin takes 3 minutes bake
time and the very-berry muffins take 1 minute bake time. The oven is only available for 1 hour (60 min) each day.
• To meet demand Mr. Thibodeau must make at least
6 chocolate chip muffins and 9 very Berry muffins
• If Mr. Thibodeau sells the chocolate chip muffins for $2.00 each and the very-berry muffins for $2.25
each, what is the maximum profit he can expect to make? Include your graph with the solution.

Answer 1

To maximize the profit, we need to determine the number of chocolate chip muffins and very-berry muffins Mr. Thibodeau should make.

Let's represent the number of chocolate chip muffins by x and the number of very-berry muffins by y.

Constraints:
1) Mix time constraint: 4x + 3y ≤ 120
2) Bake time constraint: 3x + y ≤ 60
3) Demand constraint: x ≥ 6 and y ≥ 9

Objective function:
Profit = 2x + 2.25y

To solve this problem graphically, we need to plot the feasible region determined by the constraints and find the corner points within that region.

Here is the graph showing the feasible region and the corner points:

(in the graph, x-axis represents the number of chocolate chip muffins, and y-axis represents the number of very-berry muffins)

Since the objective function is linear, the maximum profit will occur at one of the corner points.

Corner points within the feasible region:
A: (6, 57)
B: (6, 60)
C: (24, 0)
D: (30, 0)
E: (35, 0)
F: (43, 0)

By substituting the values into the objective function, we can calculate the profit for each corner point:

Profit at point A = 2(6) + 2.25(57) = $131.50
Profit at point B = 2(6) + 2.25(60) = $135.00
Profit at point C = 2(24) + 2.25(0) = $48.00
Profit at point D = 2(30) + 2.25(0) = $60.00
Profit at point E = 2(35) + 2.25(0) = $70.00
Profit at point F = 2(43) + 2.25(0) = $86.00

Therefore, the maximum profit Mr. Thibodeau can expect to make is $135.00 when he makes 6 chocolate chip muffins and 60 very-berry muffins.