Rocky Mountain Tire Center sells 6 comma 000 go-cart tires per year. The orderin
ID: 362574 • Letter: R
Question
Rocky Mountain Tire Center sells
6 comma 000
go-cart tires per year. The ordering cost for each order is
$40
,
and the holding cost is
40
%
of the purchase price of the tires per year. The purchase price is
$26
per tire if fewer than
200
tires are ordered,
$19
per tire if
200
or more, but fewer than
5 comma 000
,
tires are ordered, and
$13
per tire if
5 comma 000
or more tires are ordered.
Rocky Mountain Tire Center sells 6,000 go-cart tires per year. The ordering cost for each order is $40, and the holding cost is 40% of the purchase price of the tires per year. The purchase price is $26 per tire if fewer than 200 tires are ordered, $19 per tire if 200 or more, but fewer than 5,000, tires are ordered, and $13 per tire if 5,000 or more tires are ordered Rocky Mountain's optimal order quantity is units enter your response as a whole number b) What is the total cost of this policy? Total annual cost of ordering optimal order size-S(round your response to the nearest whole number). ).Explanation / Answer
Annual demand (D) = 6000 tires
Ordering cost (S) = $40
Holding cost (H) = 40% of price
Order size price Holding cost
Less than 200 $26 $10.4
200-5000 $19 $7.6
5000 or more $13 $5.2
First we have to find the minimum point for each price starting with the lowest price until the feasible minimum point is located.
Minimum point for the price of $13= sqrt of (2DS /H)
= sqrt of [(2 x 6000 x 40) / 5.2]
= 304 tires.
A's 304 tires will coat $19 instead of $13,it is not a feasible point for the price of $13
Next, the minimum point for price of $19 = sqrt of (2DS /H)
= sqrt of [(2x6000x40) / 7.6]
= 251 tires
Order quantity of 251 tires is feasible as it falls in the $19 per tire range of 200-5000. Now we have to calculate the total cost for 251 tires and compare it to the total cost of minimum quantity necessary to obtain a price of $13 per Tyre.
For Q= 251,Total cost = Ordering cost+carrying cost+product cost
= [(D/Q) S] + [(Q/2)H] + (price x D)
= [(6000/251)40] + [(251/2)7.6] + (19x6000)
= $956 + $954 + $114000
= $115910
The minimum order quantity to obtain a price of $13 is 5000 units.
So for Q=5000 units,
Total cost = Ordering cost+Holding cost +product cost
= [(D/Q) S] + [(Q/2)H] + (price x D)
= [(6000/5000)40] + [(5000/2)5.2] + (13 x 6000)
= $48 + $13000 + $78000
= $91048
a) Rocky Mountain's optimal order quantity is 5000 units as it has the lowest total cost.
b) The annual cost of ordering optimal order size is $91048.
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