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.

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.