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)) squared + 300 models the bakeries profits, in dollars, where x is the price of a load of bread in dollars. the bakery wants to. maximize its profits. a). what is the domain of this function? can x ever be negative? explain. b). find the daily profit for selling the bread at $2.00 per loaf. c). what price should the bakery change to maximize its profits? d). what is the maximum profit?

Given profit function where y gives profit when x is the price of a load of bread in dollars.

Ans(a):

Domain means what values of x can be taken for given function so that function is defined.

Since x represents the price of a load of bread in dollars which can't be negative in practice.

So domain will be all positive real numbers. We can also write x>0

x can't be negative.

Ans(b):

Plug x=2 into given equation.

Hence profit when load of bread is sold at $2 is $293.75.

Ans(c):

Given function is quadratic and we know that maximum occurs at the vertex of quadratic function.

compare given quadratic equation with , we get:

h=1.75 and k=300

For quadratic equation , vertex is given by (h,k)

Hence vertex for given equation is (1.75,300)

Hence bakery should change selling price to $1.75 in order to get maximum profit.

Ans(d):

Maximum profit as per above calculation is $300.

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