the brick oven bakery sells more loaves of bread when it reduces its price, but then its profits change. the function y=-100(x-1.75)^2+300 models the bakery's profits, in dollars, where x is the price of a loaf of bread in dollars. the bakery wants to maximize its profits a.) What is the domain of the function? Can x ever be negative? B.) Find the daily profit for selling the bread at $2.00 per loaf; at $1.25 per loaf. C.) What price should the bakery charge to maximize its profits? D.) What is the maximum profit?

Question

the brick oven bakery sells more loaves of bread when it reduces its price, but then its profits change. the function y=-100(x-1.75)^2+300 models the bakery's profits, in dollars, where x is the price of a loaf of bread in dollars. the bakery wants to maximize its profits      a.) What is the domain of the function? Can x ever be negative?        B.) Find the daily profit for selling the bread at $2.00 per loaf; at $1.25 per loaf.       C.) What price should the bakery charge to maximize its profits?       D.) What is the maximum profit?

aum · Answer

$y=-100(x-1.75)^2+300$  ---- (1)
a) Since x is the price of a loaf of bread it cannot be negative.  The bakery can choose to give the bread away for free and take a loss in which case x = 0.  So I'd say the domain is x > 0 and x cannot be negative.
b) put x = 2 in (1) and compute y.  Then put x = 1.25 and compute y.

aum · Answer

c) The given equation is a parabola that opens downward.  The equation is already given in the vertex form and so you can easily find the vertex which will be the top most point on the graph of the parabola.  The x-coordinate of the vertex will represent the price the bakery should charge for maximum profit and the y-value will represent the maximum profit.

anonymous · Answer

Thank you!