Answer:
no of box per production is 1000
Explanation:
given data
produces and sells = 5,000 boxes
fixed cost = $200
additional cost = $2 per box
full year costs = $2
to find out
optimal number of boxes of playing cards the company should make during each production run
solution
we consider optimal number of box is x
so
yearly storing cost = yearly storage cost per item × average no of item carried
yearly storing cost = 2 × [tex]\frac{x}{2}[/tex] = x
and
yearly recording cost = cost during each order × no of order place per year
yearly recording cost = 200 + 2x × [tex]\frac{5000}{x}[/tex]
so
total cost = x + ( 200 + 2x ) × [tex]\frac{5000}{x}[/tex]
C(x) = x + [tex]\frac{1000000}{x}[/tex] + 10000
so for minimum cost
C'(x) = 1 + [tex]\frac{1000000}{x^2}[/tex] = 0
x = 1000
so no of box per production is 1000
