A producer of pottery is considering the addition of a new plant to absorb the b

Question

A producer of pottery is considering the addition of a new plant to absorb the backlog of demand that now exists. The primary location being considered will have fixed costs of $12,480 per month and variable costs of $0.99 per unit produced. Each item is sold to retailers at a price that averages $1.18

a) The volume per month is required in order to break even = Blank 1 (in whole number)

b) The profit or loss would be realized on a monthly volume of 61,000 units = Blank 2

c) The volume is needed to obtain a profit of $16,000 per month = Blank 3 (in whole number)

d) The volume is needed to provide revenue of $23,000 per month = Blank 4 (in whole number)

Explanation / Answer

For x units of production and sale,

Cost function:

C(x) = 0.99x + 12480

Revenue function:

R(x) = 1.18x

So,

Profit function:

P(x) = R(x) - C(x) = 1.18x - (0.99x + 12480)

P(x) = 0.19x - 12480

a) In case of break even,

P(x) = 0

So,

0.19x - 12480 = 0

x = 12480/ 0.19

x = 65684.21

So,

Volume per month is required in order to break even is 65684

b) For x = 61000,

P(x) = 0.19(61000) - 12480 = -890

So,

The profit or loss would be realized on a monthly volume of 61,000 units = -890

c) For P(x) = 16000

0.19x - 12480 = 16000

0.19x = 16000 + 12480

0.19x = 28480

x = 28480/ 0.19

x = 149894.74

So,

The volume is needed to obtain a profit of $16,000 per month = 149895

d) R(x) = 23000

1.18x = 23000

x = 23000/1.18

x = 19491.53

So,

The volume is needed to provide revenue of $23,000 per month = 19492

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