# Break even, Normal Distribution, Simulation, Forecasting, LP

1. Funkia Mina is a convenient store located in Goderich and sells a wide variety of supplies. The manager of the store has noticed that several delivery services near Goderich make frequent deliveries. As such, the manager is considering selling burgers at the store. He could buy pre-made burgers and heat them in an oven. The cost of the oven and freezer would be $36,000. The frozen pizzas cost $5.00 each to buy from a distributor and to prepare (including labor and packaging). To be competitive with the local delivery services, the manager believes he should sell the burgers for $11.95 a piece. The manager needs to write up a proposal for the company's director of auxiliary services.

a. Determine how many burgers would have to be sold to break even.

b. If the Funkia Mina sells 25 burgers per day, how many days would it take to break even?

c. The manager of the store anticipates that once the local burger delivery services start losing business they will react by cutting prices. If after a month (30 days) the manager has to lower the price of a burger to $10.60 to keep demand at 25 burgers per day, as he expects, what will the new break-even point be, and how long will it take the store to break even?

2. SLET, a phone company, has collected the following frequency distribution for the length of international calls.

Length (min) Frequency

0-5 65

5-10 188

10-15 348

15-20 262

20-25 92

25+ 45

Total 1,000

The sample mean for this distribution is 35.8 minutes and the sample standard deviation is 9.2 minutes. Determine if these data are normally distributed at a significance level of alpha = 0.05.

3. The time between arrivals at a pharmacy drive through window is given by the following probability distribution.

Time Between Arrivals (minutes) Probability

1 0.05

2 0.10

3 0.19

4 0.30

5 0.20

6 0.10

7 0.05

1.00

The time required to serve a customer is given by the following probability distribution.

Time to Serve Customer (minutes) Probability

3 0.15

4 0.20

5 0.35

6 0.30

1.00

Simulate the arrival of customers at the pharmacy for the first 20 arrivals. Compute

a. the average time between arrivals.

b. the average waiting time before service.

c. the average number of customers waiting to be served.

4. Aureol Tobacco Company had the following average monthly sales (in millions of dollars) for the past 10 months:

Month Sales ($'000,000)

1 47.0

2 47.9

3 51.0

4 49.8

5 50.4

6 49.4

7 51.2

8 52.0

9 50.4

10 52.6

Compute the exponentially smoothed forecast with alpha = 0.40, the adjusted exponential smoothing forecast with alpha = 0.40 and beta = 0.30, and the linear trend line forecast. Compare the accuracy of the three forecasts and indicate which forecast appears to be most accurate.

5.

(i) The maximization or minimization of a quantity is the

a. goal of management science.

b. decision for decision analysis.

c. constraint of operations research.

d. objective of linear programming.

(ii) Decision variables

a. tell how much or how many of something to produce, invest, purchase, hire, etc.

b. represent the values of the constraints.

c. measure the objective function.

d. must exist for each constraint.

(iii) Which of the following is a valid objective function for a linear programming problem?

a. Max 5xy

b. Min 4x + 3y + (2/3)z

c. Max 5x2 + 6y2

d. Min (x1 + x2)/x3

(iv) Which of the following statements is NOT true?

a. A feasible solution satisfies all constraints.

b. An optimal solution satisfies all constraints.

c. An infeasible solution violates all constraints.

d. A feasible solution point does not have to lie on the boundary of the feasible region.

Questions are attached.

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