A toy manufacturer uses approximately 32,000 silicon chips annually. The chips a
ID: 462870 • Letter: A
Question
A toy manufacturer uses approximately 32,000 silicon chips annually. The chips are used at a steady rate during the 240 days a year that the plant operates. Annual holding cost is S3 per chip, and ordering cost is $120. Determine The optimal order quantity. The number of workdays in an order cycle. A small manufacturing firm uses roughly 3,400 pounds of chemical dye a year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The supplier has just announced that orders of 1,000 pounds or more will be filled at a price of $2 per pound. The manufacturing firm incurs a cost of $100 each time it submits an order and assigns an annual holding cost of 17 percent of the purchase price per pound. Determine the order size that will minimize the total cost. If the supplier offered the discount at 1,500 pounds instead of 1,000 pounds, what order size would minimize total cost? D = 3,400 pounds per year S = $100 per order H = .17P A HOTEL uses approximately 600 bars of soap each day, and this tends to be fairly constant. Lead time for soap delivery is normally distributed with a mean of six days and a standard deviation of two days. A service level of 90 percent is desired. Find the ROP. How many days of supply are on hand at the ROP?Explanation / Answer
Annual Chips
32000
Operating Days
240
Annual Holding Cost/chip
$ 3.00
Ordering Cost
$ 120.00
a).a
Optimal Order Quantity
EOQ Explained
$ 38,40,000.00
Annual Chips * Ordering Cost
$ 76,80,000.00
2 * Annual Chips * Ordering Cost
2560000
2 * Annual Chips * Ordering Cost / Ordering Cost
1600
Square Root of 2 * Annual Chips * Ordering Cost / Ordering Cost
a.b
Number of workdays in an order cycle
240
Ordering Days or working days in a Year
32000
Annual chips required for 240 days
1600
Optimal Order Quantity
12
Optimal Order Quantity Divided by Annual Chips, Multiplied by Ordering Days
b) a.
Order Size that will minimize the total Cost
680000
2*Ordering Cost per unit* Die Used per Year
$ 13,33,333
2*Ordering Cost per unit* Die Used per Year Divided by Holding Cost
1155
Square Root of 2*Ordering Cost per unit* Die Used per Year Divided by Holding Cost
b)b.
If the supplier offered the discount at 1500 pounds instead of 1000 pounds, what order size will minimize total cost?
D=3400 , S= $100, H=.17percent
We know that EOQ =1155
Therefore TC=HQ/2+SD/Q+PD
We know that P is at 3 and also at 2. Thus we will calculate both
TC ( Q = 1155 , P = 3) = 0.51(1155)/2 + 100(3400)/1155 + 3(3400)
Therefore, TC = 294.5 + 294.5 + 10200 = 10789
Now at 1500 pounds
TC ( Q = 1500 , P = 2) = 0.51(1500)/2 + 100(3400)/1500 + 2(3400)
TC = 382.5+226.7 +6800 = 7409.2
c)a.
ROP or Re-order Point
c = 600 bars per day
Service Level = 90%, Z = +1.28, Lead Time = 6 days and Standard Deviation = 2 days
Thus, answer will be 600*6+1.28*(600)*(2) = 5136
Therefore the Reorder point will be at 5136 bars of soap
c)b.
Since Re-order point is at 5136 bars of soap and usage is 600 bars/day. In approx 9 days
Annual Chips
32000
Operating Days
240
Annual Holding Cost/chip
$ 3.00
Ordering Cost
$ 120.00
a).a
Optimal Order Quantity
EOQ Explained
$ 38,40,000.00
Annual Chips * Ordering Cost
$ 76,80,000.00
2 * Annual Chips * Ordering Cost
2560000
2 * Annual Chips * Ordering Cost / Ordering Cost
1600
Square Root of 2 * Annual Chips * Ordering Cost / Ordering Cost
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