Question

Stacy sells large and small homemade pizzas. A small pizza has 10 olive pieces and 15 mushroom pieces. A large pizza has 15 olive pieces and 45 mushroom pieces. She has 60 olive pieces and 135 mushroom pieces. Stacy makes $1.50 in profit from each small pizza sold and $2.50 in profit from each large pizza sold.Which set of inequalities represents the constraints in this situation? Let x equal the number of small pizzas and let y equal the number of large pizzas.10x+15y≤6015x+45y≤135x≥0y≥01.5x+15y≤602.5x+45y≥135x≥0y≥010x+15y≥6015x+45y≤135x≥0y≥010x+15y≤6015x+45y≤135x≤1.5y≤2.5

Answer 1

- Let x be the number small pizzas and y be the number of large pizzas.

- We are told that small pizzas have 10 olive pieces and the large pizzas have 15 olive pieces and that there are a total of 60 olive pieces. This means that she cannot make use of more that 60 olive pieces, but she can use less than 60.

- Thus, we have that:

`10x+15y\le60`

- Next, we are told that small pizzas use 15 mushroom pieces, large pizzas use 45 mushroom pieces, while, there are a total of 135 mushroom pieces. Using the same logic as before:

`15x+45y\le135`

- Lastly, we are told that $1.50 from each small pizza and $2.50 from each large pizza.

- But we also know that Stacy makes small and large pizzas, thus, we know that they can either be 0 or less.

- That is,

`x\ge0,y\ge0`