Gardening Magic produces quality gardening tools for the home gardener. Its prod
ID: 392883 • Letter: G
Question
Gardening Magic produces quality gardening tools for the home gardener. Its production capacity for a certain gardening tool is 16,000 units. Gardening Magic estimates the annual demand for this tool at 6,000 units. The cost to set up the production line is $2,345, and the annual holding cost is $20 per unit. Currently, Gardening Magic produces 500 of these tools each month.
A. What is the optimal production lot size?
B. How many production runs should be made each year? What is the recommended cycle time?
C. Would you recommend changing the current production lot size from the monthly 500-unit run? Why or why not?
D. What is the projected savings of your recommendations from Question C in dollars? And the projected savings as a percentage?
USE MICROSOFT EXCEL AND SHOW FORMULAS
Explanation / Answer
Demand (D) = 6000
Set up cost (S) = 2345
Holding cost (H) = 20
production (p) = 16000 units
a) Optimal quantity (EOQ) = sqrt(2*D*S/H)*sqrt(p/(p-D)) = sqrt(2*6000*2345/20)*sqrt(16000/(16000-6000)) = 1500.4 Hence 1500 units
b) Number of production run = D/EOQ = 6000/1500 = 4
Recommended cycle time = 12 months/Number of production run = 12/4 = 3 months
c)
Imax = EOQ/p*(p-u) = 1500*(16000-6000)/16000 = 937.5
Total cost = Imax/2*H + D/EOQ*S = 937.5/2*20 + 6000/1500*2345 = 18755 $
Imax for EOQ = 500 is Imax = 500*(16000-6000)/16000 = 312.5
Total cost = Imax/2*H + D/EOQ*S = 312.5/2*20 + 6000/500*2345 =31265
As the Total cost is lower for new production lot size, so it is recommended to go for 1500 units rather than 500 units
d) Projected saving = 31265-18755 = 12510
% Saving = Project saving/Total cost as per earlier EOQ*100 = 12510/31265*100 = 40%
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