Question

The marginal cost function of producing q mountain bikes is Upper C Superscript prime Baseline left-parenthesis q right-parenthesis equals StartFraction 600 Over 0.3 q plus 5 EndFraction. (a) If the fixed cost in producing the bicycles is dollar-sign 2300, find the total cost to produce 30 bicycles. Enter an answer to two decimal places. dollar-sign 4359.23 (b) If the bikes are sold for dollar-sign 220 each, what is the profit (or loss) on the first 30 bicycles? Enter an answer to two decimal places. dollar-sign 2240.77 (c) Find the marginal profit on the 31st bicycle. Enter an answer to two decimal places. dollar-sign

Answer 1

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