# mathematics

1. Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality

2. In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project j is selected, xj = 0, otherwise) the constraint x1 – x2 ≤ 0 implies that if project 2 is selected, project 1 cannot be selected

3. In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.

4. Excel can be used to simulate systems that can be represented by both discrete and continuous random variables

5. A cycle is an up and down movement in demand that repeats itself in less than 1 year

6. If we are solving a 0-1 integer programming problem, the constraint *x*1 = *x*2 is a conditional constraint

7. A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. The conservative (maximin) strategy is

8. Events that cannot occur at the same time in any trial of an experiment are

9. An equation or inequality that expresses a resource restriction in a mathematical model is called _____________________.

10. In a break-even model, if all of the costs are held constant, how does an increase in price affect the model

11. In linear programming problems, multiple optimal solutions occur

12. Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the objective function

13. Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the constraint on money to invest

14. The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem. Which additional resources would you recommend to be increased

15. Given the following linear programming problem that minimizes cost.

Min Z = 2x + 8y

Subject to 8x + 4y ≥ 64

2x + 4y ≥ 32

y ≥ 2

What is the sensitivity range for the third constraint, y ≥ 2

16.In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest.

An appropriate part of the model would be

17.Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demands for gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1

18.In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation

19.The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write the constraint that indicates they have to use at least three of the five machines in their production

20.A professor needs help from 3 student helpers to complete 4 tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below. Which of the following constraints represents the assignment for student A

21.Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to 2.

Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. Supply is less than demand, so this is an unbalanced transshipment model. Which constraint represents the quantity shipped to retail outlet 6.

22.Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. What percentage of the students will take between 2 and 6 minutes to find a parking spot in the main parking lot

23. Jack is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. The decisions of each university have no effect on each other. This means that they are

24.Consider the following graph of sales. Which of the following characteristics is exhibited by the data

25. For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of

26.__________ moving averages react more slowly to recent demand changes than do __________ moving averages

27.A bakery is considering hiring another clerk to better serve customers. To help with this decision, records were kept to determine how many customers arrived in 10-minute intervals. Based on 100 ten-minute intervals, the following probability distribution and random number assignments developed

Number of Arrivals Probability Random number

6 0.1 0.1- 0.10

7 0.3 0.11 – 0.40

8 0.3 0.41- 0.70

9 0.2 0.71 – 0.90

10 0.1 0.91 – 0.00

Suppose the next three random numbers were .18, .89 and .67. How many customers would have arrived during this 30-minute period

28.Suppose that a production process requires a fixed cost of $50,000. The variable cost per unit is $10 and the revenue per unit is projected to be $50. Find the break-even point

29.Joseph is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. What is the probability that Jim will not be accepted at either university? *(Note: write your answer as a probability, with two decimal places. If necessary, round to two decimal places. For instance, a probability of 0.252 should be written as 0.25)*

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30.Carter’s Bed & Breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $1050 per month and the revenue they receive from each booked room is $150. What is the variable cost per occupied room? *(Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write $105.00). *

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31.Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

Formulation:

Let x = number of tractors produced per period

y = number of lawn mowers produced per period

MAX 30x + 30y

subject to 2 x + y ≤ 60

2 x + 3y ≤ 120

x ≤ 45

x, y ≥ 0

The graphical solution is shown below

What is the shadow price for fabrication? Write your answers with two significant places after the decimal and do not include the dollar “$” sign

32. Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.

Formulation:

Let x = number of tractors produced per period

y = number of lawn mowers produced per period

MAX 30x + 30y

subject to 2 x + y ≤ 60

2 x + 3y ≤ 120

x ≤ 45

x, y ≥ 0

The graphical solution is shown below

What is the shadow price for assembly? Write your answers with two significant places after the decimal and do not include the dollar “$” sign