(a) Consider an input-output model with three sectors. The input require- men for three sectors are given in the following table: Sector 1 Sector 2 Sector 3 units of sector 1 goods units of sector 2 goods units of sector 3 goods 0.1 0.2 0.1 0.3 0.2 0.2 0.2 0.1 Suppose the final demands for the three goods are 85, 95, and 20 units, respec- lively. Using your knowledge from matrices, find the number of units that should be produced in all the sectors. Find A when (A- 31,)" = -2 %3D
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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelectronic firms: A, B, and C. The quality-control department of the company has determined that 3% of the microprocessors produced by firm A are defective, 4% of those produced by firm B are defective, and 1.5% of those produced by firm C are defective. Firms A, B, and C supply 35%, 20%, and 45%, respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?1. A fruit juice producer conducted a study at a large supermarket to determine the possible influence of different package designs on the sales volume of their one-liter cartons of pure apple juice. The apple juice was sold in pyramid-shaped cartons for the first eight weeks, after which the same product packaged in barrel-shaped cartons was sold for a further eight weeks. Weekly sales (in cases) were recorded over each eightweek period. Pyramid 27 16 25 32 20 22 26 22 Barrel 25 28 34 28 22 35 18 29 Assume weekly sales are normally distributed for each carton design and that population variances are equal. If the marketer’s decision is to choose the package design that is likely to lead to large national sales, on average, should they use the barrel-shaped carton design? Conduct a hypothesis test at the 1% level of significance to determine if the mean weekly sales of pure apple juice in the barrel-shaped carton design are greater than the mean weekly sales in the pyramid-shaped…
- 1. A company needs to locate a distribution facility somewhere between the source of raw materials in Los Angeles, CA and the market for the product in Chicago, IL. Using Hoover's Transport Curves Theory and the information below, which city should the ditribution center be located in? Inbound costs Outbound costs Las Vegas, NV $ 3,000,000 $ 39,000,000 Denver, CO $ 15,000,000 $ 34,000,000 Des Moines, IA $ 22,000,000 $ 18,000,000 Rockford, IL $ 37,000,000 $ 6,000,000 A. Las Vegas, NV B. Des Moines, IA C. Rockford, IL D. Denver, COThis exercise requires the use of technology.Four sectors of the U.S. economy are (1) livestock and livestock products, (2) other agricultural products, (3) forestry and fishery products, and (4) agricultural, forestry, and fishery services. Suppose that in 1977 the input-output table involving these four sectors was as follows (all figures are in millions of dollars).Determine how these four sectors would react to an increase in demand for livestock (Sector 1) of $1,000 million, how they would react to an increase in demand for other agricultural products (Sector 2) of $1,000 million, and so on. (Round your answers to two decimal places. Let the columns of the matrix be given in millions of dollars.) To 1 2 3 4 From 1 11,937 9 109 855 2 26,649 4,285 0 4,744 3 0 0 439 61 4 5,423 10,952 3,002 216 Total Output 97,795 120,594 14,642 47,473Exercise 13-4 (LO13-2) The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows. Number ofAssemblers One-HourProduction (units) 2 15 4 25 1 10 5 40 3 30 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Draw a scatter diagram. Please state exact coordinates Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Compute the coefficient correlation. (Negative values should be…
- The production planning period for flat-screen moni-tors at Louisiana’s Roa Electronics, Inc., is 4 months. Cost data are as follows:Regular-time cost per monitor $ 70Overtime cost per monitor $110Subcontract cost per monitor $120Carrying cost per monitor per month $ 4 For each of the next 4 months, capacity and demand for flat-screen monitors are as follows: PERIOD MONTH 1 MONTH 2 MONTH 3 a MONTH 4Demand 2,000 2,500 1,500 2,100CapacityRegular time 1,500 1,600 750 1,600Overtime 400 400 200 400Subcontract 600 600 600 600aFactory closes for 2 weeks of vacation.CEO Mohan Roa expects to enter the planning period with 500monitors in stock. Back ordering is not permitted (meaning, forexample, that monitors produced in the second month cannot beused to cover first month’s demand). Develop a production planthat minimizes costs using the transportation method.This exercise requires the use of technology.Four sectors of the U.S. economy are (1) livestock and livestock products, (2) other agricultural products, (3) forestry and fishery products, and (4) agricultural, forestry, and fishery services. Suppose that in 1977 the input-output table involving these four sectors was as follows (all figures are in millions of dollars).Determine how these four sectors would react to an increase in demand for livestock (Sector 1) of $2,500 million, how they would react to an increase in demand for other agricultural products (Sector 2) of $2,500 million, and so on. (Round your answers to two decimal places. Let the columns of the matrix be given in millions of dollars.) To 1 2 3 4 From 1 11,937 9 109 855 2 26,649 4,285 0 4,744 3 0 0 439 61 4 5,423 10,952 3,002 216 Total Output 97,795 120,594 14,642 47,473 Answer will be 4x4 matrix.This exercise requires the use of technology.Four sectors of the U.S. economy are (1) livestock and livestock products, (2) other agricultural products, (3) forestry and fishery products, and (4) agricultural, forestry, and fishery services. Suppose that in 1977 the input-output table involving these four sectors was as follows (all figures are in millions of dollars).Determine how these four sectors would react to an increase in demand for livestock (Sector 1) of $2,500 million, how they would react to an increase in demand for other agricultural products (Sector 2) of $2,500 million, and so on. (Round your answers to two decimal places. Let the columns of the matrix be given in millions of dollars.)
- Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computerized wheel alignment and balancing machine. Managers feel that maintenance expense is related to usage of the machine, and they have collected the following information on weekly usage of the machine (in hours) and annual maintenance expense (in hundreds of dollars) from 10 other companies that own the machine.Company Weekly Usage(hours) Annual maintenance Expense(hundreds of dollars)A 13 17.0B 10 22.0C 20 30.0D 28 37.0E 32 47.0F 17…The accountant of Royal Products provided the following information for purposes of determining the optimal product mix: Product King (K) Product Queen (Q) Marginal income per unit R30 R36Machine hours required per unit 6 6Marginal income per machine hour R5 R6Ranking in terms of machine hours 2nd 1stLabour hours required per unit 3 6Marginal income per labour hour R10 R6Ranking in terms of labour hours 1st 2ndAnnual demand for product in units 12 000 15 000Labour hours available per annum 65 000 Machine hours available per annum 82 000 Required: Determine the optimal product mix by means of the application of linear programming techniques. (Hint: Start with your objective function and all necessary constraints.)SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.