In linear programming problems, multiple optimal solutions occur when constraints are parallel to each other. In general, an increase in price increases the break even point if all costs are held constant. A change in the value of an objective function coefficient will always change the value of the optimal solution. In an unbalanced transportation model, supply does not equal demand and supply constraints have ≤ signs. In a total integer model, all decision variables have integer solution values. In a transshipment problem, items may be transported from destination to destination and from source to source. A binomial probability distribution indicates the probability of observing r failures in n trails before observing the first success. The maximin criterion maximizes the minimum regret. Validation of a simulation model occurs when the true steady state average results have been reached. Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality. Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model? If the price decreases but fixed and variable costs do not change, the break even point Consider the following linear program: MAX z = 5x + 3y s.t. y – x ≤ 1 x ≤ 1 The optimal solution Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint? The following is an Excel “Answer” and “Sensitivity” reports of a linear programming problem. The Answer Report: The Sensitivity Report: Which additional resources would you recommend to be increased? 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? Compared to blending and product mix problems, transportation problems are unique because The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. The constraint for ingredient 3 is: If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a __________ constraint. 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? The assignment problem constraint x31+x32+x33+x34 ≤ 2 means 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. Which constraint represents the quantity shipped to retail outlet 6? Mutually exclusive events are 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. 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 strategy is: 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. If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is: In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution. 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. Given an actual demand of 59, a previous forecast of 64, and an alpha of .3, what would the forecast for the next period be using simple exponential smoothing? Consider the following graph of sales. Which of the following characteristics is exhibited by the data? Students are organizing a "“attle of the Bands"”contest. They know that at least 100 people will attend. The rental fee for the hall is $150 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? Write your answers with two significant places after the decimal and do not include the dollar “$” sign. Consider the following linear program, which maximizes profit for two products, regular (R), and super (S): MAX 50R + 75S s.t. 1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R + 0.5 S ≤ 300 paint (hours) Consider the following linear program, which maximizes profit for two products, regular (R), and super (S): MAX 50R + 75S s.t. 1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R + 0.5 S ≤ 300 paint (hours) .16R + 0.4 S ≤ 100 inspection (hours) Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows: Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Write your answers with two significant places after the decimal and do not include the dollar “$” sign. Find the optimal Z value for the following problem. Do not include the dollar “$” sign with your answer. Max Z = x1 + 6x2 Subject to: 17x1 + 8x2 ≤ 136 3x1 + 4x2 ≤ 36 x1, x2 ≥ 0 and integer If x is normally distributed with a mean of 10 and a standard deviation of 3, then find P(x ≤ 6). Round your result to four significant places after the decimal. An investor is consider 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below. Economic Condition Poor Average Good Excellent Investment (S1) (S2) (S3) (S4) A 50 75 20 30 B 80 15 40 50 C -100 300 -50 10 D 25 25 25 25 Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Round your answer to the nearest integer. The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? Do not include the dollar “$” sign with your answer. The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$” sign with your answer. Recent past demand for product ZXT is given in the following table. Month Actual Demand February 20 March 22 April 33 May 35 June 31 July 48 August 41 The forecasted demand for May, June, July, August, and September are 25, 30, 33, 38, and 40 respectively. Determine the value of MAD. Round your result to four significant places after the decimal.