71) The shipping problem in LP is also called the A) production mix problem. B) freight train problem. C) transportation problem. D) land and sea problem. E) None of the above 72) When applying linear programming to diet problems, the objective function is usually designed to A) maximize profits from blends of nutrients. B) maximize ingredient blends. C) minimize production losses. D) maximize the number of products to be produced. E) minimize the costs of nutrient blends. 73) Which of the following statements is true regarding the labor planning problem? A) It is typically a maximization problem. B) Required labor hours translate into less-than-or-equal-to constraints. C) The decision variables can include how many full- and part-time workers to use. D) The problem is only unique to banks. E) None of the above 74) Which of the following statements is false regarding the portfolio selection problem? A) The typical objective is to maximize the expected return on investment. B) The constraints only pertain to risk. C) Typical applications include banks, mutual funds, investment services, and insurance companies. D) The problem typically includes both greater-than-or-equal-to and less-than-or-equal-to constraints. E) The problem can also factor in legal requirements. 75) What is the objective in the truck loading problem? A) minimize trucking distance B) minimize the weight of the load shipped C) maximize the value of the load shipped D) minimize the cost of the load shipped E) None of the above 76) What is the objective in the diet problem? A) maximize nutrition B) minimize number of ingredients C) minimize calories D) minimize cost E) None of the above 77) What are the decision variables in the diet problem? A) amount of each ingredient to use B) number of ingredients to use C) amount of each type of food to purchase D) number of items of food to purchase E) None of the above 78) Cedar Point amusement park management is preparing the park’s annual promotional plan for the coming season. Several advertising alternatives exist: newspaper, television, radio, and displays at recreational shows. The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium. Given an advertising budget of $250,000, how many placements should be made in each medium to maximize total audience exposure? Formulate this as a linear programming problem. Type Cost Maximum number Exposure (1000s) Newspaper 1500 100 80 Television 2200 50 120 Radio 750 50 45 Shows 150 3 10 79) A computer start-up named Pear is considering entering the U.S. market with what they believe to be a smaller and faster computer than some of the existing products on the market. They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product. They want to collect a reasonable sample from across the U.S. representative of all age brackets. They have split the United States into 2 regions: East and West. They want at least 65% of their sample to cover the East and no fewer than 25% of the West. They also have divided the age groups into 3 categories: 18-35, 36-69, and 70 and up. They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69. The costs per person surveyed is given in the table below: Region 18-35 36-69 70 and up East $2.50 $2.00 $1.50 West $3.50 $3.00 $2.00 Assume that at least 1,000 people are to be surveyed. The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements. Formulate this problem as a linear program. 80) A computer start-up named Pear is considering entering the U.S. market with what they believe to be a smaller and faster computer than some of the existing products on the market. They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product. They want to collect a reasonable sample from across the U.S. representative of all age brackets. They have split the United States into 2 regions: East and West. They want at least 65% of their sample to cover the East and no fewer than 25% of the West. They also have divided the age groups into 3 categories: 18-35, 36-69, and 70 and up. They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69. The costs per person surveyed is given in the table below: Region 18-35 36-69 70 and up East $2.50 $2.00 $1.50 West $3.50 $3.00 $2.00 Assume that at least 1,000 people are to be surveyed. The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements. Find the optimal solution and minimum cost. 81) A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120, while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed six times the number of tables. Formulate this as a linear programming problem. Carefully define all decision variables. 82) A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120, while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed six times the number of tables. How many tables and chairs should the furniture manufacturer produce to maximize profit? 83) Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $150 while the profit per chair is $100. Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed 6 times the number of tables. Formulate this as a linear programming problem. Carefully define all decision variables. Find the solution. 84) A manufacturer of microcomputers produces four models: Portable, Student, Office, and Network. The profit per unit on each of these four models is $500, $350, $700, and $1000, respectively. The models require the labor and materials per unit shown below. Portable Student Office Network Total Labor (hrs/week) 5 5 6 8 4000 Chassis (unit/week) 1 1 1 1 400 Disk Drive (unit/week) 2 1 2 1 300 Hard Disk (unit/week) 0 0 0 1 20 Memory Chip (unit/week) 16 8 32 64 22,000 Circuit Bds. (unit/week) 1 1 2 4 10,000 Formulate this product mix problem using linear programming. 85) A manufacturer of microcomputers produces four models: Portable, Student, Office, and Network. The profit per unit on each of these four models is $500, $350, $700, and $1000, respectively. The models require the labor and materials per unit shown below. Portable Student Office Network Total Labor (hrs/week) 5 5 6 8 4000 Chassis (unit/week) 1 1 1 1 400 Disk Drive (unit/week) 2 1 2 1 300 Hard Disk (unit/week) 0 0 0 1 20 Memory Chip (unit/week) 16 8 32 64 22,000 Circuit Bds. (unit/week) 1 1 2 4 10,000 How many of each model should be produced to maximize profit. What is the maximum profit? 86) Ivana Miracle wishes to invest up to her full inheritance of $300,000, and her goal is to minimize her risk subject to an expected annual return of at least $30,000. She has decided to invest her money in any of three possible ways—CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 15 percent; and a money market mutual fund, which is expected to return 8 percent. Risk factors are 1.0 for the CDs, 3.6 for the stocks, and 1.8 for the money market fund. Formulate this as a linear program. 87) Ivana Miracle wishes to invest up to her full inheritance of $300,000, and her goal is to minimize her risk subject to an expected annual return of at least $30,000. She has decided to invest her money in any of three possible ways—CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 15 percent; and a money market mutual fund, which is expected to return 8 percent. Risk factors are 1.0 for the CDs, 3.6 for the stocks, and 1.8 for the money market fund. What is the optimal solution and minimum risk value? 88) A fast food restaurant uses full-time and part-time help to meet fluctuating demand during the day. The following table presents projected need for workers at different times of the day: Time Workers needed 9:00-10:00 4 10:00-11:00 5 11:00-12:00 9 12:00-1:00 10 1:00-2:00 8 2:00-3:00 4 3:00-4:00 3 4:00-5:00 6 There is a maximum of four full-time workers and the other workers are part-time workers. Each full-time worker is there from 9:00 until 5:00, while the part-time workers will work for 4 consecutive hours at a cost of $4.00 per hour. The cost of the full-time worker is $50 per day. The company wishes to minimize total cost while meeting the demands. Formulate this as a linear programming problem. Carefully define all decision variables. 89) First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return. Investment Opportunity Rate of Return Municipal Bonds 0.095 High Tech Stock 0.146 Blue Chip Stock 0.075 Federal Bonds 0.070 The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, 25 percent Blue Chip Stock, and no more than 15 percent High Tech Stock. Formulate this portfolio selection problem using linear programming. 90) Dr. Malcomb Heizer wishes to invest his retirement fund of $2,000,000 so that his return on investment is maximized, but he also wishes to keep the risk level relatively low. He has decided to invest his money in any of three possible ways: CDs that pay a guaranteed 4 percent; stocks that have an expected return of 14 percent; and a money market mutual fund that is expected to return 18 percent. He has decided that the total $2,000,000 will be invested, but any part (or all) of it may be put in any of the three alternatives. Thus, he may have some money invested in all three alternatives. He has also decided to invest, at most, 30 percent of this in stocks and at least 20 percent of this in money market funds. Formulate this as a linear programming problem and carefully define all the decision variables