Answer:
(a) It will take Jones 25 hours to produce a finished book of 150 pages
(b) The marginal cost of the 150th page of the finished book is $4
The marginal cost of the 300th page of the finished book is $8
Explanation:
q=[tex]S^{1/2}[/tex][tex]J^{1/2}[/tex] = [tex]\sqrt{SJ}[/tex]
q = the number of pages in the finished book
S = the number of working hours spent by Smith
J = the number of hours spent working by Jones.
For first draft, smith works for 900 hours at $3 per working hour
q = [tex]\sqrt{900J}[/tex]
q=[tex]\sqrt{900}[/tex] × [tex]\sqrt{J}[/tex]
q = 30 × [tex]\sqrt{J}[/tex]
[tex]\frac{q}{30}[/tex] = [tex]\sqrt{J}[/tex], squaring both sides we have,
([tex]\frac{q}{30}[/tex])² = J
(a) Since Jones has to produce a book of 150 pages and Smith worked 900 hours on it,
q = 150, S = 900 , J = ?
J = ([tex]\frac{150}{30}[/tex])² = 5²
J = 25
Therefore, it would take 25 hours for Jones to produce a book of 150 pages.
(b) ([tex]\frac{q}{30}[/tex])² = J
Since Smith worked for 900 hours at $3 per working hour, his total cost of work is = 900 × $3 = $2,700.
Jones total cost of work at $12 per working hour = $12J
Total cost of work, C = $2,700 + $12J
C = $2,700 + $12([tex]\frac{q}{30}[/tex])²
Marginal cost, MC = [tex]\frac{dC}{dq}[/tex]
= [tex]\frac{d}{dq}[/tex] [$2,700 + $12([tex]\frac{q}{30}[/tex])²]
= [tex]\frac{4q}{150}[/tex]
if q = 150, MC = [tex]\frac{4*150}{150}[/tex]
= $4
if q = 300, MC = [tex]\frac{4*300}{150}[/tex] = $8
