final

MSB 701 Final Exam

Professor Masele Kibassa Lehman College

Please show all work to receive credits…. 1. In your own words: What is inventory? What is the objective of Inventory Control? What are the two most

important questions (with meanings) a manager is seeking answer when going to the process of trying to

control inventory? For 15 points

(You have the page to fill)

2. Linear programming: Please use the graphical model to solve this problem. For 15 points.

A Nutritionist wants to put together a Lunch menu for certain Nursing Homes’ long term occupants. The menu

is to include two items A and B. Suppose that each ounce of A provides 2 units of vitamin C and 2 units of iron

and each ounce of B provides 1 unit of vitamin C and 2 units of iron. Suppose the cost of A is 4¢/ounce and the

cost of B is 3¢/ounce. Since Item B was purchased under difficult negotiation contact, at least 1 ounce of it

must be present per serving. If the lunch menu must provide at least 8 units of vitamin C and at least 10 units of

iron, how many ounces of each item should be provided in order to meet the iron and vitamin C requirements

to minimize cost? What will this lunch cost?

What is the objective function? What are the limitations (inequalities)?

Please provide a display showing interactions among limitations

What is the best combination of number of ounces of food A and B that should be considered to minimize Cost?

What is the minimum cost?

3. For 15 points. Given the following Quantity Discount Schedule

Discount Number Discount quantity Discount % Discount cost ($)

1 0 to 299 0 $36

2 300 to 599 1.5 To be completed

3 600 to 999 2.5 To be completed

4 1000 or more 3 To be completed

If the normal cost per unit is $ 36, the ordering cost per order is $55; the annual demand is 6000 units, and the holding cost is 33 % of the cost per unit. What order quantity will minimize the total inventory cost? Please show all work

4. Christina motor Company uses 15750 (Yearly Demand) air filters during the span of a year, and this usage is

relatively constant throughout the year. These air filters are bought from a supplier 150 miles away for $25 each,

and it takes 5 days from ordering to receipt. The carrying cost per unit per year is 22% of the unit cost and the

ordering cost per order is $47. There are 210 working days per year. For 15 points

a. What is the Economic Order Quantity (round to the nearest whole number)?

b. What is the average inventory?

c. About how many orders per year would be placed (round to the nearest whole number)?

d. What is the total Annual inventory cost (Not just the total annual ordering and holding, but also including

purchased cost of air filter)?

e. What is the Lead-time?

f. What is the Re-ordering point? (think)

5. For 15 points. The distribution of the ages of adults in Gino follows a normal pattern with a mean of 49 years

old and a standard deviation of 7.5 years. Given the above information, compute the following:

a. The probability that a randomly selected adult inhabitant of this town is older than 59 years of age

b. The probability that a randomly selected adult inhabitant of this town is older than 40 years of age

c. The probability that a randomly selected adult inhabitant of this town is between 49 and 69 years of age

d. What age will separate the top 22% to the rest of the population?

e. What ages separate the middle 78 % to the rest of the population

6. For 25 points. Given the table below X Y

a. Draw a scatter diagram and speculate on the direction linear relationship between the two variables

b. Find the coefficient of correlation (r) and Comment on it (Please use complete sentences to respond)

c. Compute the coefficient of determination(R2) and tell us what it means (Please use complete sentences to respond)

12 22

8 16

6 13

10 16

13 21

5 10

7 13

d. Find the equation of the regression line.

e. Use the equation and make a prediction of your choice that make sense. Is this prediction reliable at 0.05?