**CAPACITY PLANNING PROBLEMS**

- The Crystal Sparkle Co. produces glass tumblers. The plant is designed to produce 400 tumblers per hour, and there is 1 eight-hour shift per working day. However, the plant does not operate for the full 8 hours: the employees take two 15-minute breaks in each shift, one in the first 4 hours and one in the second 4 hours, the first 30 minutes of the shift are spent raising the kilns to the required temperature for firing glass. The plant usually produces about 10,000 tumblers per five-day workweek. Answer the following questions by adjusting the data
**to one eight-hour shift**. - What is the design capacity in tumblers?
- What is the effective capacity in tumblers? As a percent?
- What is the actual output in tumblers?
- What is the efficiency ratio?
- What is the utilization ratio?

- Suppose a manufacturer makes bicycles composed of a body, a steering wheel and two wheels. Demand for the bicycles is 500 a week. The wheel production capacity is 1200 wheels a week, the the steering wheel production capacity is 450 a week, and the final assembly department can produce 550 bicycles a week.

a) What is the capacity of the factory?

b) What limits the throughput of the factory?

c) How many wheels should be produced each week?

d) What is the utilization of wheel production operation?

e) What happens if the utilization in wheel production department is increased to 100%?

- The selling price of the product is $199.95. The variable costs per unit are:

Labor / $60.25

Raw material / 25.70

Purchased component / 21.50

Variable overhead / 17.50

The fixed costs total $300,000 per year. Perform a breakeven analysis of this company.

- What is the total revenue function?
- What is the total cost function?
- What is the profit function?
- What is the breakeven point in units of the product?
- What is the revenue at the breakeven point?
- What is the income at the breakeven point?
- Estimate the profit when 9,000 units of the product are sold in a year.
- How many units must be sold for the company to make $900,000?
- $75,000 in a year?

4. A small grocery store has a total of **four regular checkout lines and one express checkout line**. Recently on Sundays the store has been experiencing either excessive idle time for cashiers or excessively long customer waiting lines. The results of a recent time study performed by a management consulting company showed that the average service time for express and regular checkout lines are 3 and 10 minutes, respectively. As the next step in analyzing the problem, the manager of the grocery store wants to determine the estimated capacity of the store on Sundays in terms of total number of customers. Currently the store is open from 6 a.m. to midnight on Sundays. The express checkout line is always open while there is only one regular line open from 6 a.m. to 9 a.m. and also one regular line open from 9 p.m. to midnight. There are two regular checkout lines open from 9 a.m. to noon and also from 6 p.m. to 9 p.m. All four regular lines are open between noon and 6 p.m.

a.Determine the current capacity of the store in total number of customers for Sundays.

b.Assume that the store manager decides to reduce the number of regular lines from 2 to 1 between 7 p.m. and 9 p.m. and closes the express line between 6 a.m. and 8 a.m. and 10 p.m. and midnight. What is the revised capacity for Sundays?

5. A video equipment manufacturer produces videotapes and DVDs. The manufacturing facility operates two eight-hour shifts per day for 6 days a week. The unit manufacturing time is 6 minutes for each videotape and 8 minutes for each DVD.

a.Given that machine operators work at 80% efficiency, determine the number of workers needed to produce 5000 videotapes and 2500 DVDs per week.

b.Given that machines have 95% efficiency, determine the number of machines needed to produce 5000 videotapes and 2500 DVDs per week.

c.Assume that the number of workers is sufficient, what is the maximum number of videotapes and the maximum number of DVDs that can be manufactured with 15 machines.

d.Assume that the number of machines is sufficient, what is the maximum number of videotapes and the maximum number of DVDs that can be manufactured with 20 workers.