Answer:
a) $3
b) $2
c) 1449
Explanation:
Given:
The cost for a carton of milk = $3
Selling price for a carton of milk = $5
Salvage value = $0 [since When the milk expires, it is thrown out ]3
Mean of historical monthly demand = 1,500
Standard deviation = 200
Now,
a) cost of overstocking = Cost for a carton of milk - Salvage value
= $3 - $0
= $3
cost of under-stocking = Selling price - cost for a carton of milk
= $5 - $3
= $2
b) critical ratio = [tex]\frac{\textup{cost of under-stocking }}{\textup{cost of overstocking + cost of under-stocking }}[/tex]
or
critical ratio = [tex]\frac{\textup{2}}{\textup{3 + 2}}[/tex]
or
critical ratio = 0.4
c) optimal quantity of milk cartons = Mean + ( z × standard deviation )
here, z is the z-score for the critical ration of 0.4
we know
z-score(0.4) = -0.253
thus,
optimal quantity of milk cartons = 1,500 + ( -0.253 × 200 )
= 1500 - 50.6
= 1449.4 ≈ 1449 units
