The Pizza Man is a local shop that plans to make all of its sales this Saturday from its sidewalk tables during the town’s holiday parade. On this occasion, the shop’s owners know that customers will buy by the slice and any kind of pizza offered will sell. The Pizza Man offers plain, meat, vegetable, and supreme pizzas. Each variety has its own requirement for sauce, cheese, dough, and toppings (in ounces, as shown in the table), and each has its own selling price. Plain Meat Vegetable Supreme Available Dough 5 5 5 5 200 Sauce 3 3 3 3 90 Cheese 4 3 3 4 120 Meat 0 3 0 2 75 Veggies 0 0 3 2 40 Price $8 $10 $12 $15 The Pizza Man expects to use its entire stock of ingredients and wishes to maximize revenue from its sales. (a) What mix of pizzas should be made? (Assume that fractions can be sold.) (b) What is the maximum sales revenue? (c) Which ingredients are economically scarce (limit profits)?
Using AMPL program
The Pizza Man is a local shop that plans to make all of its sales this Saturday from its sidewalk tables during the town’s holiday parade. On this occasion, the shop’s owners know that customers will buy by the slice and any kind of pizza offered will sell. The Pizza Man offers plain, meat, vegetable, and supreme pizzas. Each variety has its own requirement for sauce, cheese, dough, and toppings (in ounces, as shown in
the table), and each has its own selling price.
Plain Meat Vegetable Supreme Available
Dough 5 5 5 5 200
Sauce 3 3 3 3 90
Cheese 4 3 3 4 120
Meat 0 3 0 2 75
Veggies 0 0 3 2 40
Price $8 $10 $12 $15
The Pizza Man expects to use its entire stock of ingredients and wishes to maximize revenue from its sales.
(a) What mix of pizzas should be made? (Assume that fractions can be sold.)
(b) What is the maximum sales revenue?
(c) Which ingredients are economically scarce (limit profits)?
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