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Garden Variety Flower Shop uses 670 clay pots a month. The pots are purchased at $2.40 each. Annual carrying costs per pot are estimated to be 10 percent of cost, and ordering costs are $10 per order. The manager has been using an order size of 2,000 flower pots. a. What additional annual cost is the shop incurring by staying with this order size? (Round your optimal order quantity to the nearest whole number. Round all other intermediate calculations and your final answer to 2 decimal places. Omit the "$" sign in your response.)Additional annual cost $_____________b. Other than cost savings, what benefit would using the optimal order quantity yield (relative to the order size of 2,000)? (Use the rounded order quantity from Part a. Round your final answer to the nearest whole percent. Omit the "%" sign in your response.) About ________ % of the storage space would be needed.

Respuesta :

Answer and Explanation:

For computing the additional cost and the percentage of the storage space first we have to determine the economic order quantity and the total cost which is shown below:

Economic order quantity

[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]

[tex]= \sqrt{\frac{2\times \text{8,040}\times \text{\$10}}{\text{\$0.24}}}[/tex]

= 819 units

The annual demand is

= 670 per month × 12 months

= 8,070

And, the carrying cost is

= $2.40 × 10%

= $0.24

Now The total cost of ordering cost and carrying cost based on economic order quantity

= Annual ordering cost + Annual carrying cost

= Annual demand ÷ Economic order quantity × ordering cost per order + Economic order quantity ÷ 2 × carrying cost per unit  

=  8,070 ÷ 819 × $10 + 819 ÷ 2 × $0.24

= $98.53 + $98.28

= $196.81

And,  The total cost of ordering cost and carrying cost based on order size

= Annual ordering cost + Annual carrying cost

= Annual demand ÷ Economic order quantity × ordering cost per order + Economic order quantity ÷ 2 × carrying cost per unit  

=  8,070 ÷ 2,000 × $10 +2,000 ÷ 2 × $0.24

= $40.35 + $240

= $280.35

So the cost saving is

= $280.35 - $196.81

= $83.54

And we Assume that 2,000 units occupied the 100%  space

Hence, 1 unit will occupy

= 1 ÷ 2,000

= 0.05% of the space

Therefore  in case of economic order quantity the percentage will occupy

= 819  × .05

= 40.95% of the space  i.e 41%

And, in case saving of space is 59 in case of ordering of economic order quantity rather than order size i.e 2,000 units