The table below shows the cost CC to Company A , in dollars, of selling xx cups

Question

The table below shows the cost CC to Company A, in dollars, of selling xx cups of coffee per day from a cart.

a) Assuming the function CC is linear. What is the slope of the line corresponding to the graph of y=C(x)y=C(x)?
The line has slope =

b) The value for C(200)C(200) is missing in the table above. In the blank provided in the table, enter the correct value for C(200)C(200) assuming the cost is a linear function of xx.

Now consider Company B , whose cost FF, in dollars, of selling xx cups of coffee per day from a cart is given in the table below:

c) Which company pays higher fixed costs for rent and labor?
A. Company A
B. Company B

d) Which graph will be steeper, the graph corresponding to Company A's cost C(x) , or the graph corresponding to Company B's cost F(x)
A. Company A
B. Company B

Explanation / Answer

a)

Since it is given that the given function is linear so its linear equation is of the form > y=mx+c

now we have from the table that xx(0) has cc(50) and when xx(5) has cost cc(50.75). It means that 5 cups cost 0.75 giving us cost for 1 cup = $0.15 which is the required slope. slope of 0.15 means that for every 1 cup the cost will go up $0.15.

b)

Now our linear equation becomes y = 0.15x + c

Now by putting any known x and y (0, 50) or (5, 50.75) and upon solving c comes to be 50. So finally our equation becomes y = 0.15x + 50.

Now for xx = 200 (x) the cost cc (y) is :

y = 0.15*200 + 50 or cost = $30

c)

Now for company B, we can prepare a linear equation in the same way as we have done above in case of company A.

it is > y = 0.10x + 55

As we can see by comparing linear equations for both the companies that fixed expenses 'c' for company B is 55 > 50 of company A.

So company B pays higher fixed costs for rent and labor.

d)

The graph corresponding to Cost will be steeper which has greater slope value.

Company A has 0.15 > Company B has 0.10

so Company A is answer.

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