Question

Pizzeria Duo Express sells two type of pizzas; regular and deluxe. The company sells each regular pizza for $7 and each deluxe pizza for $10. The firm currently has 150 pounds of dough mix and 50 pounds of topping mix. Accounting reports that the current amounts of dough and topping mix have a value of $300 and $125, respectively. 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. Based on the past demand per week, Bryant can sell at least 50 regular pizzas and at least 25 deluxe pizzas, on a regular day.

A. Formulate the standard form of this model.

B. Determine the number of regular and deluxe pizzas the company should make to maximize net income, each day.

Answer 1

Cost of 1 pound of Dough mix = $300/ 150 pounds = $2 and Cost of 1 pound of topping mix = 125/ 50 = $2.5 and cost of 4 ounces of topping mix = $2.5/16*4 = $0.625

Therefore, cost of one regular pizza = cost of 1 pound of dough mix + cost of 4 ounces of topping mix = $2 + $0.625 = $2.625

and cost of one deluxe pizza = cost of 1 pound of dough mix + cost of 8 ounces of topping mix = $2 + 2 * $0.625 = $3.25

Therefore, Profit from a regular pizza = $7 - $2.625 = $4.375 and profit from a deluxe pizza = $10 - $3.25 = $6.75

Now, we understand that no. of pizzas that can be made from dough mix is 150

No. of regular pizzas which can be made from the available topping mix is 50*(16/4) = 200 and maximum no. of deluxe pizzas can be 50*(16/8) = 100.

therefore topping mix is the limiting factor,

thus Contribution per 4 ounce of topping mix on making regular pizza is $3.25

and contribution per 4 ounce of topping mix on making deluxe pizza is $6.75/2 = $3.375

Net profit on making maximum regular pizzas , i.e. 150 regular pizzas = 150*3.25 = $487.5

and Net profit on making maximum deluxe pizzas , i.e. 100 deluxe pizzas = 100*6.75 = $675.

Thus, we should only make deluxe pizzas.