Question

Can someone plzz help its a long question
A coffee shop pays Coffee Delivery Company A, a certain price for each disposable cup it orders plus a weekly delivery charge to remain on the driver’s delivery route. The cups are purchased in increments of 500. To quickly determine how much the coffee shop will be spending on cups before their arrival, the owner created the following table:

Answer 1

Cups Ordered Price
0 $7
500 $25.50
1,000 $44
1,500 $62.50
2,000 $81
2,500 $99.50
3,000 $118

A. The price of the cups, p(x), is a function of the number of x cups ordered. Using the table, determine the average rate of change for the first 1,000 cups ordered and then for all 3,000 cups ordered. What does this tell you about the function?

B. Use the table to evaluate and interpret p(0). What is a possible explanation for this?

C. Sketch a graph, labeling its key features, to show the price the coffee shop would pay Coffee Delivery A to have between 0 and 3,000 cups delivered each week.

D. Create a model using function notation that represents how the two quantities, cups and cost, are related.

E. The coffee shop found another delivery company that sells orders at increments of 500 cups, Coffee Delivery B. They charge $3.50 each week to be on their delivery route and charge 3.9 cents per disposable cup.

I.Make a function using the information about the second delivery company.

II.Using a different color to add to the graph sketched in Part C, graph the price the coffee shop would pay for Coffee Delivery B to deliver the same amount of cups.

III.If the coffee shop can change delivery companies every three months, when should they consider Coffee Delivery A, and when should they consider Coffee Delivery B?

Answer 2

p(x) = (0.037)x + (7.00)

the cost per cup is: $0.037

the function is linear

the average rate of change is: (0.037) [the slope of the function !]

Answer 3

They pay $18.5 for every 500 cups plus a $7 weekly delivery charge.
The graph would be a straight line beginning at (0,7) and going through all the given points to (3000,118)

Answer 4

Company A:
f(c) = 18.50(c/500) + 7
f(c) = 0.037c + 7<====ANSWER
where f(c) is cost and c is cups

Company B:
f(c) = 0.039c + 3.5

Obviously, company B will be cheaper for a few cups, but eventually their price will exceed company A's. To find where that point is, set the equations equal to each other:
0.037c + 7 = 0.039c + 3.5
3.5 = 0.002c
17500 = c

So, if they expect to need less than 17500 cups, go with company B; if they expect to need more than 17500 cups, use company A.