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The marginal cost function of producing q mountain bikes is 600/0.3q+5.

If the fixed cost in producing the bicycles is 2200 , find the total cost to produce 30 bicycles.

If the bikes are sold for 205 each, what is the profit (or loss) on the first 30 bicycles?

Find the marginal profit on the 31st bicycle. ...?

Verified Answer :

syed514

MArginal cost is the adjustment in all out cost that emerges when the amount created changes by one unit.(In another word subordinate of cost wrt unit) 
So we coordinate to get Cost work 
∫30 600/0.3q+5 (dq) 0
we get 9798.66 from joining. 
We add that to settle cost 2059.23+2200=4259.24 
So 4259.24 is the cost. 
Income from offering the bicycle is 205*30=6150 
and Profit=Revenue-Cost 
6150 - 4259.24=1890.76 
Presently Marginal Profit 
MArginal benefit is the term used to allude to the contrast between the minor cost the peripheral income for delivering one extra unit of creation. 
Marginal Profit=Marginal Revenue-Marginal Cost 
Marginal Cost=600/0.3q+5. 
We should connect to 31 to get 41.958 
Revenue= 205q 

Marginal rev=205 
Marginal Profit = 205-41.958=163.042

The total cost to produce 30 bicycles is 4259.23, the profit is 1890.77, and the marginal profit on the 31st bicycle is 163.05.

What is a marginal cost?

It is defined as the cost showing an increase in the cost when the number of units produced increases In simple words it is the ratio of the cost to quantity.

We have the marginal cost function of producing q mountain bikes is:

\(\rm C'(q) = \frac{600}{0.3q+5}\)

For the total cost = fixed cost + cost for producing 30 bikes

\(=2200+\rm \int_{0}^{30}\frac{600}{0.3q+5}dq\)

The value of the definite integration:

\(\rm \int_{0}^{30}\frac{600}{0.3q+5}dq = 2059.23\)  

= 2200+2059.23

= 4259.23

For the profit or loss:

Profit = revenue - cost

Profit = 205×30 - 4259.23 ⇒ 6150 - 4259.23 ⇒ 1890.77

For the marginal profit on the 31st bicycle:

Marginal Profit = Marginal Revenue - Marginal Cost

Marginal cost  \(= \frac{600}{0.3\times 31+5}\) ⇒ 41.95

Marginal revenue on the 31st bike = 205

Marginal Profit = 205 - 41.95 ⇒ 163.05

Thus, the total cost to produce 30 bicycles is 4259.23, the profit is 1890.77, and the marginal profit on the 31st bicycle is 163.05

Learn more about the marginal cost here:

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