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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