Question

PLEASE HELP MEEE HURRYY (Make sure to show your work)

A grocer sells 50 loaves of bread a day. The cost is $0.65 a loaf. The grocer estimates that for each $0.05 price increase, 2 fewer loaves of bread will be sold. What cost will maximize the profit?
Let x = number of $0.05 price increases

What is the equation to represent the single price

What is the equation for the number of loaves sold

What is the equation for the income.

Find the vertex.

What cost will bring the maximum profit.

Answer 1

Let's first define some variables:

Let P be the selling price of one loaf of bread in dollars (not including any price increases).

Let x be the number of $0.05 price increases.

Let Q be the number of loaves sold per day.

Let R be the revenue (income) per day.

Let C be the cost per day (the cost of the 50 loaves sold).

Using the given information, we can set up the following equations:

The selling price, P, can be written as:

P = 0.65 + 0.05x

The number of loaves sold, Q, can be written as:

Q = 50 - 2x

The revenue per day, R, can be written as:

R = P * Q

R = (0.65 + 0.05x) * (50 - 2x)

The cost per day, C, is simply:

C = 50 * 0.65

C = 32.50

The profit per day, which is the difference between revenue and cost, is:

Profit = R - C

Profit = (0.65 + 0.05x) * (50 - 2x) - 32.50

To find the vertex, we can either complete the square or use calculus. Let's use calculus:

Profit' = -0.1x^2 + 2.5x - 32.5

Setting Profit' = 0 and solving for x gives:

x = 12.5

Therefore, the vertex is at x = 12.5.

To find the cost that will maximize profit, we need to find the corresponding selling price:

P = 0.65 + 0.05x

P = 0.65 + 0.05(12.5)

P = 1.30

Therefore, the selling price that will maximize profit is $1.30 per loaf.

Explanation: