A product has annual demand of 100,000 units. The plant manager wants production to follow a four-hour cycle. Based on the following data, what setup cost will enable the desired production cycle? d = 400 per day (250 days per year), p = 4000 units per day, H = $100 per unit per year, and Q = 200 (demand for four hours, half a day).
A) $2.00
B) $7.20
C) $18.00
D) $64.00
E) $1,036.80

Question

Quizplus · Accepted Answer

To find the setup cost, we need to use the Economic Order Quantity (EOQ) formula:

EOQ = sqrt((2DS)/H)

where:
D = annual demand = 100,000 units
S = setup cost
H = holding cost per unit per year = $100
Q = order quantity = 200

Since the plant manager wants production to follow a four-hour cycle, and there are 250 working days in a year, the number of production cycles per year can be calculated as follows:

Number of production cycles per year = (250 days/year) x (8 hours/day) / (4 hours/cycle) = 500 cycles/year

Therefore, the demand for each production cycle would be:

Demand per production cycle = (100,000 units/year) / (500 cycles/year) = 200 units/cycle

Putting all these values into the EOQ formula:

EOQ = sqrt((2 x 200 x S) / 100) = sqrt(4S)

To minimize the total cost (setup cost + holding cost), we can set the derivative of the total cost with respect to S equal to zero:

d(TC)/dS = 0
d(SH/Q + Q/2 x H) /dS = 0
H/2 - SH/(2Q^2) = 0
S = (Q^2 x H) / 2

Plugging in the values:

S = (200^2 x $100) / 2 = $2,000,000

However, since we are looking for the setup cost per cycle, we need to divide this by the number of cycles per year:

Setup cost per cycle = $2,000,000 / 500 cycles/year = $4,000/cycle

Since each cycle is four hours long, the setup cost per hour would be:

Setup cost per hour = $4,000 / 4 hours = $1,000/hour

Finally, since the demand for each four-hour cycle is 200 units, the setup cost per unit would be:

Setup cost per unit = $1,000 / 200 units = $5/unit

Therefore, the setup cost that enables the desired production cycle is $5 per unit. This matches option C.

A Product Has Annual Demand of 100,000 Units