Respuesta :
Answer:
$5,107.04
Explanation:
The computation of the change in the annual total cost is shown below;
Without a discount, the annual total cost is
The computation of the economic order quantity is shown below:
[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]
[tex]= \sqrt{\frac{2\times \text{720}\times \text{\$40}}{\text{\$7}}}[/tex]
= 91 units
The annual demand is
= 60 × 12 months
= 720
And, the carrying cost is
= $35 × 20%
= $7
Now The computation of the total cost is shown below:
= Purchase cost + ordering cost + carrying cost
where,
Purchase cost = Annual consumption × Cost per unit
= 720 × $35
= $25,200
Ordering cost = (Annual demand ÷ EOQ) × Cost to place one order
= (720 ÷ 91) × $40
= $316.48
Carrying cost = (EOQ ÷ 2) × carrying cost percentage × Cost per unit
= (91 ÷ 2) × 7
= $318.50
Now put these values to the above formula
So, the value would equal to
= $25,200 + $316.48 + $318.50
= $25,834.98
Now if we take the economic order be 101
So, the total cost would be
= Purchase cost + ordering cost + carrying cost
where,
Purchase cost = Annual consumption × Cost per unit
= 720 × $35 × (1 - 0.20)
= $20,160
Ordering cost = (Annual demand ÷ EOQ) × Cost to place one order
= (720 ÷ 101) × $40
= $285.14
Carrying cost = (EOQ ÷ 2) × carrying cost percentage × Cost per unit
= (101 ÷ 2) × 7 × (1 - 0.20)
= $282.80
Now put these values to the above formula
So, the value would equal to
= $20,160 + $285.14 + $282.80
= $20,727.94
Now the change in the annual total cost is
= $25,834.98 - $20,727.94
= $5,107.04
