1. A manufacturing company has a fixed cost of br. 20,000 and a variable cost of br. 10 per unit made and sold. If the company can sell what it produces at a price of br. 20 per unit:

a) Write the cost, revenue, and profit functions.

b) Determine the firm’s break-even point in terms of quantity and revenue.

c) What is the loss sustained by the firm if only 1,350 units are produced and sold each month?

d) What is the profit if 3,000 units are produced and sold each month?

e) How many units should the firm produce in order to realize a minimum monthly profit of br. 19,000?

f) Show diagrammatically the cost, revenue, and profit functions.

g) Interpret the results.

2. Ato Asfaw invests in stocks, bonds, and money market funds. The average yield is 8% on stocks, 6% on bonds, and 7% on market funds. Twice as much is invested in money market as in bonds. Moreover, the total annual return on stocks, bonds, and money market funds was br. 280,000. How much is invested in each if the total investment is br. 40,000? (Solve using a matrix)

3. (Use Graphical Method) A factory produces gasoline engines and diesel engines. Each week the factory is obligated to deliver at least 20 gasoline engines and at least 15 diesel engines. Due to physical limitations, however, the factory cannot make more than 60 gasoline engines nor more than 40 diesel engines in any given week. Finally, to prevent layoffs, a total of at least 50 engines must be produced.

a) If gasoline engines cost br. 450 each to produce and diesel engines cost br. 550 each to produce, how many of each should be produced per week to minimize the cost?

b) What is the excess capacity of the factory? That is, how many of each kind of engine is being produced in excess of the number that the factory is obligated to deliver?

4. A candy company makes three types of candy: solid, fruit, and cream filled, and packages these candies in three different assortments.

- A box of Assortment I contains 4 solid, 4 fruit, and 12 cream candies and sells for br. 9.40.
- A box of Assortment II contains 12 solid, 4 fruit, and 4 cream candies and sells for br. 7.60.
- A box of Assortment III contains 8 solid, 8 fruit, and 8 cream candies and sells for br. 11.00.

The manufacturing costs per piece of candy are br. 0.20 for solid, br. 0.25 for fruit, and br. 0.30 for cream. The company produces up to 4,800 solid, 4,000 fruit, and 5,600 cream candies weekly. How many boxes of each type should the company produce in order to maximize profit? What is their maximum profit?

**Part II: Business Statistics**

5. Consider the grouped frequency distribution:

| Weights | Frequency |
|---------|-----------|
| 40 – 50 | 7 |
| 50 – 60 | 5 |
| 60 – 70 | 8 |
| 70 – 80 | 5 |
| 80 – 90 | 11 |
| 90 – 100| 9 |

a) Find the mean, median, and mode.

b) Find the variance and standard deviation.

6. Suppose that 10% of all TVs made by A & B Company are defective. If eight of these TVs are randomly selected from across the country and tested, what is the probability that exactly three of them are defective? Assume that each TV is made independently of the others.

7. Suppose that 45% of all customers who enter a department store make a purchase. What is the probability that 2 of the next 3 customers will make a purchase?

8. The average age of a vehicle registered in Ethiopia is 12 years. Assume the standard deviation is 9 years. If a random sample of 32 vehicles is selected, find the probability that the mean of their age is between 8 and 15 years.