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xenn [34]
1 year ago
13

Hi, can you help me with this problem?A manufacturer has a monthly fixed cost of $42,500 and a production cost of $6 for each un

it produced. The product sells for $11/unit.(a) What is the cost function?C(x)= (b) What is the revenue function?R(x)=(c) What is the profit function?P(x)= (d) Compute the profit (loss) corresponding to production levels of 6,000 and 11,000 units.P(6,000)=P(11,000)=
Mathematics
1 answer:
Reika [66]1 year ago
4 0

Given:

Fixed cost = b = $ 42,500

Production cost (Variable cost) /unit = m = $ 6/ unit

Let 'x' represent the number of unit, therefore the variable cost will be

6x

a) The cost function will be the sum of the fixed cost and the variable cost.

C(x)=6x+42500

b) The revenue function is the amount the product is sold per unit.

Recall: 'x' represents the number of units.

Therefore,

11\times x=11x

Hence, the revenue function R(x) is

R(x)=11x

c) The profit function is the difference between the revenue function and the cost function.

P\mleft(x\mright)=11x-\mleft(425000+6x\mright)=5x-42500

Hence, the profit function is

P\mleft(x\mright)=5x-42500

d) Let us compute the profit (loss) values when the units are 6000 and 11000

Using the profit function

P(x)=5x-42500

Therefore,

\begin{gathered} P(6000)=5(6000)-42500=30000-42500=-\text{ \$12500} \\ P(11000)=5(11000)-42500=55000-42500=\text{ \$12500} \end{gathered}

Hence,

\begin{gathered} P(6000)=-\text{ \$12500  (which is a loss)} \\ P(11000)=\text{ \$12500  (this is a profit)} \end{gathered}

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