Problem 23 Healthy Plants Ltd. (HP) produces its premium plant food in 50-pound

Question

Problem 23 Healthy Plants Ltd. (HP) produces its premium plant food in 50-pound bags. Demand for the product is 10,000 pounds per week. HP operates fifty weeks per year and can produce 23,000 pounds per week. The setup cost is $180 and the annual holding cost rate is $0.58 per bag. Currently, HP produces its premium plant food in batches of 1,500,000 pounds Your answer is incorrect. Try again. Calculate the maximum inventory level for HP according to its current operating policy. 11564.25 pounds (Round your answer to 2 decimal places, the tolerance is +/-0.01. Do not round your intermediate computations.) Your answer is incorrect. Try again. Calculate the total annual costs of this operating policy. 7752.50

Explanation / Answer

Given,

1 bag= 50 pounds

Weekly Demand (d)=10,000 pounds per week= 10,000/50=200 bag/week

N= 50 weeks / year

Annual demand (D) = 10,000 * 50 = 5,00,000 pounds /50= 10,000 bag/year

Production per week (p)=23,000 pounds per week/50=460 bags/week

Annual production (P)= 460*50= 23,000 bags per year

Setup cost (S)=$180

Holding Cost (H) = $0.58 per bag per year

EOQ= (2DS/H)^0.5 = (2*10000*180/0.58)^0.5= 2491.36 bags

Maximum Inventory = Imax = (1-D/P)Q

            = (1 – (10000/23000))*2491.36 = 1408.16 bags

Maximum Inventory (in pounds) = 1408.16*50= 70408 pounds

Total annual cost = SD/Q + HQ/2 = (180*10000/2491.36) + ((0.58*2491.36)/2) = 722.496+722.494= $1444.99

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