Please help and show all your work Thank you!!! Prefab, a furniture manufacturer
ID: 429391 • Letter: P
Question
Please help and show all your work Thank you!!!
Prefab, a furniture manufacturer, uses 20,000 square feet of plywood per month. Its trucking company charges Prefab S400 per shipment, independent of the quantity purchased. The manufacturer offers an all umit quantity discount with a price of $1 per square foot for orders under 20,000 square feet, $0.98 per square foot for orders between 20,000 square feet and 40,000 square feet, and $0.96 per square foot for orders larger than 40,000 square feet. Prefab incurs a holding cost of 20 percent What is the optimal lot size for Prefab? What is the annual cost of such a policy? What is the cycle inventory of plywood at Prefab? How does it compare with the cycle inventory if the manufacturer does not offer a quan- tity discount but sells all plywood at S0.96 per square foot?Explanation / Answer
Name of the company : Prefab
Sector : Furniture manufacturer
Material : 20000 sq.feet plywood per month
S = Annual demand = 20000 * 12 = 240000 sq.feet
Trucking company charges : $ 400 per shipment (We will consider this as ordering cost )
Quantity discount
Case 1
0 – 20000 = $ 1 per square foot
Case 2
20001 – 40000 = $ 0.98 per square foot
Case 3
Above 40000 = $ 0.96 per square foot
Holding cost(Ch) = 20 %
Optimal Lot size = ?
Annual cost = ?
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Optimal size Q
for case 1 =
= Square root {(2 * S*Cp)/(Ch)
= Square root {(2 * 240000*400)/(0.20)
= $ 30984
Annual cost = (2 *S/Q*Cp ) + (Q/2*Ch)
=(2*240000/30984*400)+(30984/2)*0.20
=6197 + 3099
= $ 9296
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Optimal size Q
for case 2 =
= Square root {(2 * S*Cp)/(Ch)
= Square root {(2 * 240000*400)/(0.20 * 0.98)
= $ 31299
Annual cost = (2 *S/Q*Cp ) + (Q/2*Ch)
=(2*240000/31299*400)+(31299/2)*0.20*0.98
=6135 + 3068
= $ 9203
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Optimal size Q
for case 3 =
= Square root {(2 * S*Cp)/(Ch)
= Square root {(2 * 240000*400)/(0.20 * 0.96)
= $ 31623
Annual cost = (2 *S/Q*Cp ) + (Q/2*Ch)
=(2*240000/31623*400)+(31623/2)*0.20*0.96
=6072 + 3036
= $ 9108
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If manufactuer does not offer a quantity discount but sells at disocount $ 0.96 , in that case company will buy the product as per the rquirement.They will try to reduce the cost in materials. So overall cost will be decreased.