The setup cost to make a carpet is $20 per setup.The holding cost is $2.00 per yard per year,and the annual demand is 12,000 yards.The manufacturing facility operates 300 days,and 120 yards of the carpet are produced per day.Given this information,which of the following statements is true?
A)The optimal production quantity is 600.
B)The optimal production quantity is 500.
C)The optimal production quantity is 400.
D)The optimal production quantity is 300.

Question

Quizplus · Accepted Answer

The optimal production quantity can be calculated using the Economic Production Quantity (EPQ) model formula: $EPQ = \sqrt{\frac{2DS}{H(1-\frac{d}{p})}}$, where $D$ is the annual demand, $S$ is the setup cost, $H$ is the holding cost per unit per year, $d$ is the demand rate per day, and $p$ is the production rate per day. Substituting the given values: $D = 12000$ yards, $S = 20$, $H = 2$, $d = \frac{12000}{300} = 40$ yards/day, $p = 120$ yards/day, we find the EPQ is approximately 600 yards, making option A correct.

The Setup Cost to Make a Carpet Is $20 Per