1- A paint manufacturer's production process is normally distributed with a mean of 100,000 gallons and a standard deviation of 20,000 gallons. Management wants to incentive bonus for the production crew when the daily production exceeds the 95th percentile of the distribution.

i) At what level of production should management pay the incentive bonus?

ii) What is the probability that the deviation of daily production from mean being greater than 20,000 gallons?

2- A company markets educational software products and is ready to place five new products on the market. Past experience has shown that for this particular software, the chance of "success" is 90%. Assume that the probability of success is independent for each product. (10 points)

i) Find the probability that exactly 2 of the 5 products is successful.

ii) Find the probability that at least 1 product is successful.

3) Given the following linear programming problem:

Max Z = 5x + 3y

s.t.

3x + y ? 40

2x-y ? 10

What would be the values of x and y that will maximize revenue?

A) x = 13; y = 1 B) x = 13.33; y = 0 C) x = 10; y = 10 D) x = 0; y = 40

6- Sonny Lawler's law office uses EOQ models to manage their office supplies. They've been ordering ink refills for their printers in quantities of 100 units, each $20 (i.e., price of each unit is $20). The firm estimates carrying cost at 25% of its price and that annual demand is about 1000 units per year. The assumptions of the basic EOQ model are thought to apply. For what value of ordering cost would its action be optimal?

7- A bakery uses an average of 50 ounces of organic orange juice daily. Demand is normally distributed with a standard deviation of 12 ounces. The bakery places an order every thirteen days. The lead time for delivery of the juice is three days.

i) Compute the safety stock required to achieve a 90% service level.

ii) If the bakery has 160 ounces at the time an order is placed, how much should be ordered?

ECON20110/ECON30370 1. Consider the regression model: y = Xf u (a) State the Gauss-Markov assumptions required to show that the Ordinary Least Squares estimator of the coefficients is the Best Linear Unbiased Estimator (BLUE) [5 marks] [b) Prove that the OLS estimator is unbiased if the Gauss-Markov assumptions hold Show relevant steps and assumptions [10 marks] (c) Show that the variance covariance matrix of the OLS estimator is Var (8 X) -6-(XX) [5 marks]In a Salton-Watson branching process starting with a single individual in generating zero, the offspring distribution is Binomial 55. U4]. To four decimal places, the probabilities that the process becomes extinct by the second generation and extinct at the third generation are respectively Cl 0.1099. 0.0631 0.3472. 0.0631 0.1099. 0.4103 0.3472. 0.4103 Iail-hich is the correct answer? Let Xn be a Galton-Watson (Branching) process as we discussed in the class, where X 0 = 1 with probability 1. Let p; denote the expected number of offspring each individual has, and let 02