Question

John is making apple pies and apple cobblers to sell at the farmer’s market. A pie uses 4 cups of apples and 3 cups of flour. A cobbler uses 2 cups of apples and 3 cups of flour. When John sells the pies and cobblers at the farmer’s market, he will make $3.00 profit per pie and $2.00 profit per cobbler. Let x = the number of pies John makes. Let y = the number of cobblers John makes. Interpret the meaning of the vertex with the maximum profit in context of john’s baking.

Answer 1

The vertex with the maximum profit represents the optimal point at which John should produce apple pies and apple cobblers in order to maximize his profit.

Step-by-step explanation:

The vertex with the maximum profit represents the optimal point at which John should produce apple pies and apple cobblers in order to maximize his profit. The x-coordinate of the vertex represents the number of pies John makes, and the y-coordinate represents the number of cobblers John makes.

To find the vertex, we need to create an equation for the profit function. The profit from pies is 3x, where x is the number of pies, and the profit from cobblers is 2y, where y is the number of cobblers. The total profit, P, can be represented as P = 3x + 2y. Since we want to find the maximum profit, we can graph this equation and find the vertex.

Once we have the vertex, we can interpret its meaning in the context of John's baking. The x-coordinate of the vertex tells us the number of pies that John should make to maximize his profit, and the y-coordinate tells us the number of cobblers he should make.

Answer 2

Step-by-step explanation:

there are some pieces of information missing like the price of apples and flour. or the selling prices. or any restrictions like a fixed budget to buy ingredients or how many pies and cobblers he can make in a certain available time.

all we can say based on the given information :

one pie = 4a + 3f (a = apples, f = flour)

one cobbler = 2a + 3f

P(x, y) = 3x + 2y =

= x(selling price - 4a - 3f) + y(selling price - 2a - 3f)

the max. of P(x, y) is the maximum profit by selling pies and cobblers, which is without any further information +infinity.

the more pies and cobblers he sells, the bigger the profit - no limit.