SUBJECT: MATH : Quantitative Methods for Business and Finance. Course Symbol: MAT 128

Please answer the questions below.

PLEASE DO NO WORRY ABOUT THE MARKS: EXAMPLE : 2 MARKS, 3 MARKS OR 4 MARKS. BECAUSE THEY ARE NOT PART OF THE QUESTIONS

D Question 5 3 pts 5. A box contains 17 apples, with 9 of these apples bad and the rest of them good. A sample of 3 apples is selected at random. What is the probability of obtaining no bad apples in the sample? Answer this question in both of the cases below: (a) (3 marks) The sampling is done without replacement. (b) (3 marks) The sampling is done with replacement.Question 6 4 pts 6. A car rental company finds that each person that rents a car fails to show up with probability 12%, independently of other people. As a result, the car rental company always takes 15 reservations for its 12 cars. (a) (2 marks) What is the expected number of people with reservations that will show up? (b) (4 marks) Find the probability that more than 12 people with reservations show up.D Question 7 10 pts 7. A lab makes two types of test kits for Covid-19. Each rapid test kit requires 1 swab and 7 ounces of reagant and sells for $9. Each slow test kit requires 2 swabs and and 4 ounces of reagant and sells for $13. The lab has 60 swabs and 280 ounces of reagant available. (a) (8 marks) Find how many test kits of each type should be made to maximize the revenue. (b) (2 marks) Find the maximum revenue.D Question 8 5 pts 8. Assume the demand equation giving the number of barrels of oil, n, sold when the price per barrel is p dollars is linear and the following information is known: Price per barrel, p Number of barrels, n $80 40 $85 28 (a) (2 marks) Find the revenue if the price per barrel is $85. (b) (3 marks) Find the demand equation for n as a function of p. (c) (3 marks) Find the revenue equation for R as a function of n. (d) (3 marks) Find the revenue when 17 barrels of oil are sold. (e) (4 marks) Find the marginal revenue, R' (17), when 17 barrels of oil are sold. (f) (5 marks) Use calculus to find how many barrels of oil should be sold in order to maximize the revenue. What is the maximum revenue?D Question 9 3 pts 9. Assume the number of people, P, in a state that are infected with a virus is 160 on March 1, 2020 and is 290 on March 6, 2020, and is undergoing continuous exponential growth with a growth constant of k per day; that is, dt dP - KP. where t is the number of days after March 1, 2020. (a) (3 marks) Find the growth constant, k. (b) (3 marks) Use your model to predict that number of people in the state that are infected with this virus on March 20, 2020