QMB 3602 Examination #3 (a) 4. (25 points) - the annual demand is 200 units per
ID: 3315465 • Letter: Q
Question
QMB 3602 Examination #3 (a) 4. (25 points) - the annual demand is 200 units per year. The ordering cost for this line of tractors is $2,500 per order, and the carrying cost is $190 per tractor per year. RapidGrow's supplier has offered a quantity discount for this line of tractors as shown in the following table: RapidGrow Garden Implements sells a line of garden tractors for which QUANTITYPRICE 1-49 50-89 90+ $1,400 1,100 900 a) Calculate the optimal order quantity. Show all work! b) Calculate the order quantity to minimize TAC along with the corresponding TAC.Explanation / Answer
The Total cost= D/Q*c+P*D+h*Q/2, thus on differentiating we get Q=SQRT(2*c*D/h)
a)Optimal quantity =SQRT(2*2500*200/190)=72.54
b) We see the optimal quantity falls under the second category, thus price charged will be 1100.
TAC=[D/Q*c+P*D+h*Q/2]/Q=c*D/Q^2+P*D/Q+h/2, On differentiating we get -2cD/Q^3-P*D/Q^2=0, we see that Q=-2c/P, we will calculate TAC at boundary points,
At Q=49 TAC= 6017.5
At Q=89 TAC=2630.033
At Q=90. TAC=2156.72, Thus TAC decreases with Q, thus we choose Q=72 and TAC at Q=72.54 is 3222.83.
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