Homework: Homework 8 Score: 0 of 1 pt Problem 12.25 Save 70f 7 (6 complete) Hw S
ID: 365420 • Letter: H
Question
Homework: Homework 8 Score: 0 of 1 pt Problem 12.25 Save 70f 7 (6 complete) Hw Score: 85.71%, 6 of 7 pts Question Help cost s 40% of the purchase price of the tires per year he pur se price is S per re fte er than 20 Rocky Mountain Tre Center sells 1 1 00 go o tres per year. The ordering cost for each order s $4 and the hold $17 per tire if 200 or more, but fewer than 5,000, tires are ordered, and $15 per tire if 5,000 or more tires are ordered a) How many tires should Rocky Mountain order each time it places an order? ires are o ered Rocky Mountain's optimal crder quantity is 5,000 units (enter your response as a whole number). b) What is the total cost of this policy? Total annual cost of ordering optimal order siund your response to the nearest whole number)Explanation / Answer
Annual demand (D) = 11000 tires
Ordering cost (S) = $40
Holding cost (H) = 40% of price
Order size price Holding cost
Less than 200 $19 $7.6
200-5000 $17 $6.8
More than 5000 $15 $6
First we have to calculate the minimum point for each price starting with the lowest price until the feasible minimum point is located
Minimum point for $15 = sqrt of (2DS /H)
= sqrt of [(2 x11000x40) / 6]
= 383 tires
383 tires will cost $17 instead of $15.so it is not a feasible point for $15.
Minimum point for $17 = sqrt of (2DS / H)
= sqrt of [(2 x 11000 x 40) / 6.8]
= 360 tires
Order quantity of 360 tires is feasible as it falls in the $17 per tire range of 200-5000. Now we have to calculate the total cost for 360 tires and compare it to the total cost of minimum quantity necessary to obtain a price of $15 per tire.
For Q=360,
Total cost = Ordering cost + Holding cost + purchase cos
= [(D/Q) S] + [(Q /2)H] + (D x price)
= [(11000/360)40] + [(360/2)6.8] + (11000 x 17)
= $1222.22 + $1224 + $187000
= $189446.22
The minimum order quantity to obtain a price of $15 is 5000 tires. So with Q=5000,
Total cost = Ordering cost + Holding cost + purchase cost
= [(D /Q) S] + [(Q /2)H] + (D x price)
= [(11000/5000)40] + [(5000/2)6] + (11000 x 15)
= $88 + $15000 + $165000
= $180088
a) Rocky mountain's optimal order quantity is 5000 tires as it has the lowest total cost.
b) The annual cost of Ordering optimal order size is $180088
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.