you invest in a new play. the cost includes an overhead of $33,750, plus product

Question

you invest in a new play. the cost includes an overhead of $33,750, plus production costs of $2500 per performance. a sold out performance brings in $3125. (in solving this exercise, let x represent the number of sold out performance)

a. write the cost function , C.
b. write the revenue function, R. 
c. determine the break even point. describe what this means.

a. write the cost function, C. 
C(x)=____( type an expression using x as the variable)

b. write the revenue function, R. 
R(x)=____(type an expression using x as the variable)

c. determine the break even point 
______ sold out performances

describe what this means 
a. the point where the cost and revenue are equal 
b. the point where revenue and production cost are equal
c. the point where revenue and overhead cost are equal
d. the point where the cost and overhead cost are equal

Explanation / Answer

overhead cost=$33750
a) Cost of production C = overhead cost +production cost=$33,750 + 2500x
b) The revenue R = 3125*number of sold out performance=3125x
d) The break even point is where C=R or $33,750 + 2500x = 3125x
33,750 + 2500x-2500x = 3125x-2500x
33750 = 3125x-2500x
33750 = 625x
33750/625 = x
x=54
So at x=54 the revenue and overhead costs are equal
d)at x=54 the cost and overhead cost is given by 3125*54=$168,750
so our required point is (54,168750)

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