Math for business

Question

Delvecchio's pizza shop makes three specialty pizzas, the Mighty Meaty, the Very Veggie, and Super Cheesy. The Mighty Meaty is topped with 5 different meat toppings and 2 different cheeses. The Very Veggie has 6 different vegetable toppings and 4 different cheeses. The Super Cheesy has 6 different cheeses. The cost of the meat toppings for each Mighty Meaty is $3, and the cost of the vegetable toppings is $2 for each Very Veggie. No more than $60 per day can be spent on these toppings. The cheese used for the Mighty Meaty is $2 per pizza, the cheese for the Very Veggie is $4 per pizza, and the cheese for the Super Cheesy is $ 6 per pizza. No more than $480 per day can be spent on cheese . No more than 80 pizzas can be made per day due to manpower and bake time. How many pizzas of each type should Delvecchio's pizza shop make in order to maximize revenue if the Mighty Meaty sells for $15, the Very Veggie sells for $12, and the Super Cheesy sells for $12? Set up the problem, including specifically what the variables represent, the objective function and whether it is to be maximized or minimized, and all constraints. Then use the simplex method to solve the given problem. Be sure to show your initial simplex tableau and all tableaus including the final tableau. Interpret your entire answer in complete sentences. Discuss any suggestions you have to help increase their profit and cut down their cost? Type up your interpretation and discussion about suggestions on another sheet of paper.

I still get so confused with this, and this is a long question and I know it has a lot to do which it makes me confused more

Answer 1

First, the information at the beginning about how many meats and cheeses are on each type of pizza is red herring information, which is to say it has no bearing on any other part of the problem and won't help you solve it.

Per WyzAnt's guidelines, I'm not going to tell you the answer, but I'm going to offer this guidance in how to get toward it:

This is essentially a systems of equations and inequalities problem. Give each pizza type a variable (say, m, v, and c for meat, veggie, and cheese).

For every bit of helpful information you're given, create an equation or inequality. For example, if my lemonade stand makes regular lemonade (r), strawberry lemonade (s), and mango lemonade (m), and I realize I only have the capacity to make 97 cups a day due to the amount of labor I and my employees can do, then r+s+m≤97.

Each sentence provides information that can help you figure something out. You may want to make an equation or inequality considering the budget you have for toppings and another equation or inequality considering the budget you have for cheeses. Total cost for money spent on a particular product is (price per set of ingredients)*(number of products produced). For example, if it costs me $1.50 to make regular lemonade, $2 to make strawberry lemonade, and $2 to make mango lemonade, the total amount I'm spending would be 1.5r+2s+2m. And maybe I have a budget for those ingredients (say, $84) and would need to set that equal or less-than-or-equal-to to a particular amount (so 1.5r+2s+2m≤84). Maybe I pull in different kinds of profits for those lemonades based on how much I charge for them, and that's another equation or inequality.

To solve any system of equations or system of inequalities, you need at least as many equations or inequalities as you have variables to solve for. So that means you should create at least three equations or inequalities to solve this. If you're stuck on solving once you have your equations or inequalities, I'll highly recommend Khan Academy's videos on that. (This one might help, though it's with a less complicated problem: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:inequalities-systems-graphs/x2f8bb11595b61c86:modeling-with-linear-inequalities/v/interpreting-system-of-inequalities-in-context)