Answer:
The right solution is:
(a) 4,272 units
(b) $134.16
(c) $134.17
(d) $12,268.33
Explanation:
Seems that the given question is incomplete. The attachment of the complete question is provided below.
According to the question, the values are:
Annual demand,
D = 12,000
Number of days,
= 300
Daily demand,
d = [tex]\frac{12000}{300}[/tex]
= 40
Production rate,
P = 100
Ordering cost,
S = $50
Holding cost,
H = $0.10
(a)
The production run's optimal size will be:
Q = [tex]\sqrt{\frac{2DS}{H(1-\frac{d}{P} )} }[/tex]
By putting the values, we get
= [tex]\sqrt{\frac{2\times 12000\times 50}{0.10\times (1-\frac{40}{100} )} }[/tex]
= [tex]\sqrt{20,000,000}[/tex]
= [tex]4,471.14[/tex]
or,
= [tex]4,472 \ units[/tex]
(b)
The average holding cost will be:
= [tex]\frac{Q}{2}\times H\times [1-\frac{d}{P} ][/tex]
= [tex]\frac{4472}{2}\times 0.10\times [1-\frac{40}{100} ][/tex]
= [tex]134.16[/tex] ($)
(c)
The average setup cost will be:
= [tex]\frac{D}{Q}\times S[/tex]
= [tex]\frac{12000}{4472}\times 50[/tex]
= [tex]134.17[/tex] ($)
(d)
The total cost per year will be:
= [tex]Avg. \ holding \ cost+ Avg. \ setup \ cost+Cost \ of \ purchase[/tex]
= [tex]134.16+134.17+(1\times 12000)[/tex]
= [tex]12,268.33[/tex] ($)
