You are the manager of a small company producing interlocking paving pieces, cal

Question

You are the manager of a small company producing interlocking paving pieces, called pavers, for driveways. You sell the pavers in bundles that cost $200; each bundle contains 144 pavers. The total cost in dollars, C(x), of producing x bundles of pavers is modeled by C(x) = 160x+1000.

a)The revenue is the amount of money collected from the sale of the product. Write an equation for the revenue function in dollars, R, from the sale of x bundles.

b) Determine the slope and the C-intercept of the given cost function. Explain the practical meaning od each in this situation.

c) Determine the slope and the R-intercept of the revenue function. Explain the practical meaning of each in this situation.

e) Determine the exact break-even point algebrically.

f) How many bundles of pavers does the company have to sell for it to break even?

g) What is the total cost to the company when you break even? Verify that the cost and revenue values are equal at the break-even point.

h)For what values of x will your revenue exceed your cost?

i) As manager, what factors do you have to consider when deciding how many pavers to make?

j) I you could sell only 30 bundles of pavers, would you make them? Consider how much it would cost you and how much you would make. What if you could only sell 20?

Any help is appreciated! This is the only problem where I don't even know where to begin! :(

Explanation / Answer

C(x) = 160x+1000.

revenue = price* number of units sold

R(x) = 200*x

slope of cost function is 160

and C intercept is 1000

slope represent cost per bundle

breakeven point occusr when revenue = cost function

200x =  160x+1000.

40x = 1000

x = 25

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