Explanation

ai. 

C = 30 + 4q
when q = 18units

C = 30 + 4(18)
= 30 + 72
= 102 dollars

aii. 

C = 30 + 4q
when q = 36 units

C = 30 + 4(36)
= 30 + 144
= 174 dollars

bi. 

At 28 units

Average cost = \(\frac{Total Cost}{Quantity}\)

NOTE: TC = C = 30 + 4q

Therefore, AC =\(\frac{30+4q}{q}\)

= \(\frac{30+4(28)}{q}\)

=\(\frac{142}{28}\)

= 5.07 dollars

bii. 

At 45 units

Average cost = \(\frac{Total Cost}{Quantity}\)

NOTE: TC = C = 30 + 4q
 

Therefore, AC =\(\frac{30+4q}{q}\)

= \(\frac{30+4(45)}{45}\)

=\(\frac{210}{45}\)
= 4.66 dollars

c. 

Marginal cost at 28 units produced = Total cost at 28 units - Total cost at 18 units

=\(\frac{30+4(28)-30+4(18)}{28-18}\)

= \(\frac{142-102}{10}\)

= $4.00

d. 

Profit (π) = Total sales at 45 units - Total cost at 45 units
= ($5 x 45) - ( 30 + 4(45))
= 225 - 210
= $15.00

e. 

Fixed cost is zero. Fixed cost is a cost that does not change, i.e when q = 0 then C = 30 +4(0)
= C = 30 + 4(0)
= 30 + 0
= $30

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