Answer:
A. What is the optimal size of the production run for this particular compound?
first we have to determine the holding cost per unit = h = (22% + 012%) x ($3.5) = $1.19 per unit, per year
then we have to calculate the modified holding cost per year = h' = h x [1 / (D/P)] = $1.19 x [1 / (600,000/2,500,000)] = $0.9044 per unit, per year
now we have to substitute h for h' in the EOQ formula:
Q' = √ [(2 x S x D) / h'] = √ [(2 x $1,500 x 600,000) / $0.9044] = 44,612.44 ≈ 44,612 units
B. What proportion of each production cycle consists of uptime and what proportion consists of downtime?
Time between production runs = Q' / D = 44,612 / 600,000 = 0.07435333
Uptime = Q' / P = 44,612 / 2,500,000 = 0.0178448
Downtime = total time - uptime = 0.07435333 - 0.0178448 = 0.05650853
uptime = 0.0178448 / 0.07435333 = 24% of total time
downtime = 0.05650853 / 0.07435333 = 76% of total time
C. What is the average annual cost of holding and setup attributed to this item? If the compound sells for $3.90 per pound, what is the annual profit the company is realizing from this item?
average annual holding cost and setup costs = (AD/Q') + (h'Q'/2) = [($1,500 x 600,000) / 44,612] + [($0.9044 x 44,612) / 2] = $40,144
profit per unit = $3.90 - $3.50 = $0.40 per pound
total annual profit = ($0.40 x 600,000) - $40,144 = $199,856
