How many glasses of lemonade does he need to sell to break even?

Do all the following problems.

 

1. I. Choose the best answer for each multiple choice. Please use CAPITAL letters to indicate your answer and write neatly. (20 points)

 

1. ____ 3.____ 5. ____            7.____             9.____
2. ____ 4.____            6.____             8.____             10.____
3. Mickey built his lemonade stand out of $250 worth of plywood and paint. He sells a glass of lemonade for $3 and uses $1.25 of lemons, sugar and water to make his product. How many glasses of lemonade does he need to sell to break even?

 

1. 170
2. 161
3. 152
4. 143

 

2. Which of the following is not true about continuous random variables?
3. They have an infinite set of values.
4. The area under each of the curves represents probabilities.
5. They can only be integer values.
6. The entire area under each of the curves equals 1.

 

3. Which of the following will increase the breakeven point?
4. Increase selling price
5. Increase fixed cost
6. Decrease variable cost
7. Decrease fixed cost

 

4. The manager of a manufacturing company is trying to figure out how many products need to be produced for the coming quarter. Suppose the beginning inventory of the quarter is 500 units and the management predicts that the sales volume in the coming quarter would be 2400 units. The company also requires 1100 units ending inventory for the coming quarter. What should be the production volume for that quarter?
5. 3900
6. 3300
7. 3000
8. 2400

 

5. If P(A) = 0.3, P(B) = 0.2, P(A∩B) = 0, what can be said about events A and B?
6. They are independent.
7. They are mutually exclusive.
8. They are posterior probabilities.
9. They are collectively exhaustive.

 

6. A project consists of 150 jobs and the expected time for each job is given in days. The project only has three paths through it, called A, B and C, and the duration of path A is four days shorter than path B, but equal to the duration of path C. In order to finish the project one day early, the completion time should be reduced one day for
7. A. each of the three paths.
8. path A only.
9. path A and C only.
10. path B only.

 

7. Which of the following is true about the expected value of perfect information?
8. It is the amount you would pay for any sample study.
9. It is calculated as EMV minus EOL.
10. It is calculated as expected value with perfect information minus maximum EMV.
11. It is the amount charged for marketing research.

 

8. Given a linear programming model:

 

Max       6x₁ + 9x₂

s.t.          x₁    <   7

2x₁ + 3x₂  <  18

x₁, x₂ > 0

 

Which of the following statement is true?

1. The model has only one optimal solution.
2. The model has no feasible solutions.
3. The model has unbounded solution.
4. The model has multiple optimal solutions.

 

 

9. In the classic Economic Order Quantity (EOQ) associated with inventory under the assumptions of constant demand and fixed costs, what happens if the annual demand increases from 1000 units to 2000 units?
10. The EOQ increases and the reorder point increases.
11. The EOQ decreases and the reorder point decreases.
12. The EOQ increases and the reorder point remains the same.
13. The EOQ decreases and the reorder point increases.

 

 

 

10. Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average price per square foot for a home is greater than $110?
11. 0
12. 0.023
13. 0.841
14. 0.977

 

 

1. Problem Solving

 

1. Given the following linear program:

 

Max       3x₁ + 4x₂

s.t.        2x₁ + 3x₂  < 24

3x₁ + x₂  <  21

x₁, x₂ > 0

 

1. Identify the feasible region. (You must draw the feasible region.) (5 points)

 

1. Find all the extreme points – list the value of x₁ and x₂ at each extreme point. (6 points)

 

1. What is the optimal solution? (4 points)

 

 

1. Everett Mann’s Dream Store sells waterbeds and supplies. The best-selling bed in the store has an annual demand of 400 units. The ordering cost is $40, while the holding cost is $5 per unit per year. There are 250 working days per year, and the lead-time is 6 days.

 

1.  Develop a total cost model for this system. (4 points)

 

1.  What is the optimal reorder quantity? (4 points)

 

1. What is the cycle time? (4 points)

 

1. What is the reorder policy for Everett Mann’s Dream Store? (4 points)

 

1. What total annual cost does the model give? (4 points)

3. Consider the tasks, durations, and predecessor relationships in the following network. Draw the network and answer the questions that follow.

 

Activity	Immediate Predecessors	Optimistic (Weeks)	Most Likely (Weeks)	Pessimistic (Weeks)
A	—	4	7	10
B	A	5	8	11
C	A	8	12	16
D	B	1	2	3
E	D, C	6	8	10
F	C	2	3	4
G	F	2	2	2
H	F	6	8	10
I	E, G, H	4	8	12
J	I	1	2	3

 

1. Draw a project network for this problem. (5 points)

 

1. Fill in all the blanks in the following table. (10 points)

 

Note: For variance (σ²) in activity time, keep two decimal places.

 

Activity	Expected Time t (weeks)	Variance σ2	ES	EF	LS	LF	Slack	Critical Path?
A
B
C
D
E
F
G
H
I
J

1. What is the expected time and variance to complete the project? (4 points)

 

1. What is the probability of completion of the project before week 42? (4 points)

 

1. Suppose activity E were delayed for 5 weeks. By how much would the entire project be delayed? (4 points)

 

 

 

4. Suzie’s Sweatshirts is a home-based company that makes upscale, hand-painted sweatshirts for children. Forecasts of sales for the next year are

 

Autumn:   125

Winter:     350

Spring:       75

 

Each Shirt is sold for $15. The holding cost per shirt is 6% of the selling price per quarter. The shirts are painted by part-time workers who earn $4.50 per hour during the autumn. Because of the high demand for part-time help during the winter holiday season, labor rates are higher in the winter, and Suzie must pay the workers $6.00 per hour. In the spring, labor is more difficult to keep, and Suzie finds that she must pay $5.50 per hour to get qualified help. Each shirt takes 1.5 hours to complete. Formulate the problem to a LP model to help Suzie plan production over the three quarters to minimize the combined production and inventory holding cost. Suppose there is no inventory at the beginning of the autumn. (10 points)

(Note: You do not need to solve the model.)

 

 

5. The time it takes to travel from home to the office is normally distributed with m = 25 minutes and s = 5 minutes. What is the probability the trip takes between 30 and 35 minutes? (8 points)