Bryant\'s Pizza, Inc. is a producer of frozen pizza products. The company makes

Question

Bryant's Pizza, Inc. is a producer of frozen pizza products. The company makes a net income of $1.00 for each regular pizza and $1.50 for each deluxe pizza produced. The firm currently has 150 pounds of dough mix and 800 pounds of topping mix. Each regular pizza uses 1 pound of dough mix and 4 ounces (16 ounces= 1 pound) of topping mix. Each deluxe pizza uses 1 pound of dough mix and 8 ounces of topping mix.  The problem is to determine the number of regular and deluxe pizzas the company should make to maximize net income. Create a linear optimization Model

Explanation / Answer

I think you got the requirements for the regular and Deluxe Pizzas combined.

I believe a regular pizza uses .5 kg of dough mix and .125 kg of topping mix, while the deluxe pizza uses .5 kg of dough mix and .25 kg of topping mix. With these requirements, here is the linear programming you wanted:

Let x = # of regular pizzas
Let y = # of deluxe pizzas

x ? 50
y ? 25
.5x + .5y ? 70
.125x + .25y ? 25

P(x,y) = x + 1.5y

When graphed, the vertices occur at (50,25), (50,75), (80,60), or (115,25)

P(50,25) = 50 + 1.5(25) = 87.50
P(50,75) = 50 + 1.5(75) = 162.50
P(80,60) = 80 + 1.5(60) = 170.00 <==MAXIMUM INCOME
P(115,25) = 115 + 1.5(25) = 152.50

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