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Rusk Corporation sells 185,000 gallons of paint annually at several retail outle

ID: 2754313 • Letter: R

Question

Rusk Corporation sells 185,000 gallons of paint annually at several retail outlets. The ordering cost per order is $75, and its cost of capital is 10%. The storage and handling cost for paint is $2 per year, based on average inventory. Rusk buys the paint from the manufacturer according to the following price schedule: 1 - 999 gallons at $11 per gallon, 1000 - 9999 gallons at $10 per gallon, and 10,000 gallons and over at $9 per gallon.

(A) Find the optimal order quantity for Rusk.                                            10,000 gallons

(B) For this optimal order size, what is the total annual cost of paint?            $1,680,888

(C) What is the annual cost of the inventory system?                                           $15,888

Explanation / Answer

Answer:(A) Find the optimal order quantity for Rusk.

a. 185000*11=2,035,000

2*Q/2=1Q

75*185000/Q=13875000/Q

0.10*11*Q/2=0.55Q

1.55Q+13875000/Q+2035000

1.55-13875000/Q^2=0

Q=SQR13875000/1.55=10000 GALLONS

Answer:(B) 10000*9 + 2(Q/2) + 75*10000/Q + 0.10*2=1680888

Answer:(C) 10000*9 + 2(Q/2) + 75*10000/Q + 0.10*0.10= 15888