The Wod Chemical Company produces a chemical compound that is used as a lawn fertilizer. The compound can be produced at a rate of 10,000 pounds per day. Annual demand for the compound is 0.6 million pounds per year. The fixed cost of setting up for a production run of the chemical is $1,500, and the variable cost of production is $3.50 per pound. The company uses an interest rate of 22 percent to account for the cost of capital, and the costs of storage and handling of the chemical amount to 12 percent of the value. Assume that there are 250 working days in a year. A. What is the optimal size of the production run for this particular compound?
B. What proportion of each production cycle consists of uptime and what proportion consists of downtime?
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?

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

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