Manager receives a forecast for next year. demand is projected to be 600 units for the first half of the year and 900 units for

Question

29 days ago

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Manager receives a forecast for next year. demand is projected to be 600 units for the first half of the year and 900 units for

the second half. the monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order.
a. assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods.
b. why is it important to be able to assume that demand will be level during each six-month period?
c. if the vendor is willing to offer a discount of $10 per order for ordering in multiples of 50 units (e.g., 50, 100, 150), would you advise the manager to take advantage of the offer in either period? if so, what order size would you recommend

Business

1 answer:

marusya05 [3K] · Answer 1 · 2026-03-07T04:00:26+03:00

A) For the first half of the year, the monthly demand averages to 560 / 6 = 93.33
Order size for the first six months can be calculated using: Sqrt(2 x A x O / C)
Where:
O is the cost of placing an order
C is the carrying cost per order
= Sqrt(2 x 93.33 x 55 / 2) = 71.65, rounded to 72
For the second half of the year, the monthly demand is 900 / 6 = 150
Order size for the second six months:
= Sqrt(2 x A x O / C)
= Sqrt(2 x 150 x 55 / 2)
= 90.83 or 91
B) For the first six months: Total monthly cost = (Q/2) x H + (d/Q) x S= (72 / 2) x 2 + (93.33 / 72) x 5 = $143.30 With a $10 discount, S = $ 55 - $10 = $ 45
Monthly TC at Q = 50 = (50/2) x 2 + (93.33 / 50)x 45 = $134.0 Monthly TC at Q = 100 = (100/2) x 2 + (93.33 / 100) x 45 = $142.00
Monthly TC at Q = 150 = (150/2) x 2 + (93.33 / 150) x 45 = $178.00
C)
Indeed, the manager should take advantage of this proposal and order Q = 50 units for the first six months. For the second six months, d = monthly demand = 900 / 6
= 150,

H = $2.00 for each unit monthly, S = $55, & EOQ = 91.
Calculating Monthly TC (Q = 91):
= (91/2) x 2 + (150/91) x 55
= $181.66
Monthly TC (Q = 50):= (50/2)x2 + (150/50)x 45= $185 Monthly TC (Q = 100) = (100/2) x 2 + (150/100) x 45= $167.50
Monthly TC (Q = 150)= (150/2) x 2 + (150/150) x 45= $195