Question

The local Papa John's in the rural town of Gary, Indiana offered a limited amount of fantastic deals for Peyton Manning's

retirement sendoff. Deal #1 comes with 8 large pizzas and 6 orders of breadsticks. Deal #1 comes with 8 large pizzas
and 6 orders of breadsticks. Deal #2 comes with 4 large pizzas and 6 orders of breadsticks. The store will only make up
to 32 large pizzas and 30 orders of breadsticks for these deals. The profit that Papa John's makes is $22 from Deal #1
and $16 from Deal #2. Graph the constraints and determine how many of each deal Papa John's should sell to maximize
profit

Answer 1

To maximize profit, Papa John's should use linear programming to graph constraints and determine the combination of Deal #1 and Deal #2 that maximizes the profit function P = 22x + 16y, subject to constraints on the number of pizzas and breadsticks they can produce.

Step-by-step explanation:

To solve the problem of maximizing profit for Papa John's special deals, we need to use linear programming to graph the constraints and find the optimal combination of Deal #1 and Deal #2. The constraints given are that the store will only make up to 32 large pizzas and 30 orders of breadsticks.

Let's define the variables:
x = number of Deal #1s
y = number of Deal #2s

The constraints can be written as:
8x + 4y ≤ 32 (pizzas constraint)
6x + 6y ≤ 30 (breadsticks constraint)

Now, to express the profit function to maximize, it is given by:
P = 22x + 16y

To graph these constraints, we would plot each line on a graph, with the feasible region being where both inequalities are satisfied. The optimal solution (maximizing P) lies at one of the vertices of the feasible region. By evaluating the profit function at each vertex, Papa John's can determine the optimal mix of deals to maximize profit.