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- (b) A company produces 3 products A, B and C processed on 3 machines P, Q, R before completion. Machine P can process 25 units of A or 50 unit of B or 75 units of C per hour. Machine Q can process 50 units of any of the products per hour. Machine R can process 50 units of A or 25 unit of B or 100 units of C per hour. The processing hours available on machines P, Q and R are 12, 12 and 13 respectively. Use matrix method, find (i) How many units of each of the three products can be produced per day (ii) The production cost per unit, if cost per hour of operating machines A,B and C are N$500, N$1,000 and N$1,500 respectively. (iii) The total cost of production.Ronald and Son, P.A., is an auditing firm that conducts both financial and operational audits. Ronald can conduct 90 financial audits (FAs) per year if he spends full time on just FAs, or 180 operational audits (OAs) per year full time, or any linear combination of both. (Note: A linear combination means that because the capacity required for 1 FA is the same as that for 2 OAs (90 to 180 ratio), Ronald can conduct such combinations as 89 FAs plus 2 OAs, or 88 FAs plus 4 OAs, and so on.) Son processes the reports made by Ronald. Son can prepare 180 financial audit reports or 150 operational audit reports per year, or any linear combination thereof. The office staff finalizes the reports submitted by Son. They can handle no more than 160 reports of any kind, per year. Ronald and Son have calculated that to keep their association solvent, they must produce at least 30 FAs and 50 OAs each year. The profit from each FA has averaged $720 in the past and for each OA has been about $650. How…You own wheat warehouse with capacity of 20,000 bushels. At the beginning of month 1, you have 6,000 bushels of wheat. Each month, wheat can be bought and sold at the price per 1000 bushels given in the table Month Selling price ($) Purchase prie ($) 1 3 8 2 6 8 3 7 2 4 1 3 5 4 4 6 5 3 7 5 3 8 1 2 9 3 5 10 2 5 The sequence of events during each month is as follows: a. You observe your initial stock of wheat. b. You can sell any amount of wheat up to your initial stock at the current month's selling price. c. You can buy(at the current month's buying price) as much wheat as you want, subject to the warehouse size imitation. Your goal is to formulate an LP that can be used to determine how to maximise the profit earned over the next 10 months and solve using Excel solver or AMPL
- 46. Ford is going to produce a new vehicle, the Pioneer,and wants to determine the amount of annual capacityit should build. Ford’s goal is to maximize the profitfrom this vehicle over the next five years. Each vehicle will sell for $19,000 and incur a variable production cost of $16,000. Building one unit of annual capacity will cost $2000. Each unit of capacity will alsocost $1000 per year to maintain, even if the capacityis unused. Demand for the Pioneer is unknown butmarketing estimates the distribution of annual demandto be as shown in the file P09_46.xlsx. Assume thatthe number of units sold during a year is the minimumof capacity and annual demand. Which capacity levelshould Ford choose? Do you think EMV is the appropriate criterion?Show the complete Linear Programming Model. Show solutions (i.e. decision variables, objective function, subject to constraints, etc.) Q. A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $1,000 per ton to process, and ore from source B costs $500 per ton to process. Costs must be kept to less than $4,000 per day. Moreover, Government Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? Formulate the LP model.Find the minimum value of the function z=2x+2y subject to the following constraints. x≤17 y≤16 5x+2y≥42 3x+11y≥84
- Mr Sng is a retiree in his late sixties. He has $100,000 to invest. He has no regular source of income and no other assets. He is evaluating between 3 different lump-sum financial products shown in Table 3. All products require a minimum investment sum of $100,000. Monetary returns represent the net gain after one year of investing in the product. For example, if Mr Sng chose to invest in Product B, he may lose $5,000 after one year if the GDP growth is negative. He will earn $8,000 if the GDP growth exceeds 2% at the end of the year. If you were in the shoes of Mr Sng, how would you select the appropriate investment product for a time horizon of one year? (i) Use the Optimistic, Conservative and Regrets payoff analysis approaches. State which product(s) Mr Sng should invest in and what monetary return he can expect from each approach (ii) As you have only enough funds for one product, identify the most appropriate investment product. [Hint: Be sure to consider the…Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.27 In order to manufacture 3,000 pairs of shoes in a week, a firm can use 3,000 workers and 100 machines or 200 machines and 4,000 workers Which method is considered more technically efficient? a 4,000 workers and 200 machines b Both are equally efficient c 3,000 workers and 100 machines d Neither could be considered efficient 33 A manufacturing business can use 100 workers and 20 machines, 140 workers and 18 machines, or 150 workers and 18 machines to produce 80 chairs If each worker costs $40 and each machine is rented for $1000, the economically efficient input combination is: a 100 workers and 20 machines b 150 workers and 18 machines c none of these input combinations d 140 workers and 18 machines
- 19. What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 3y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x, y ≥ 0. Part 2 A. x = 0, y = 3 B. x = 2, y = 0 C. x = 0, y = 0 D. x = 0, y = 4 E. x = 1, y = 5Problem 2: Comp-Max Computers assembles computers and computer equipment. It is about to start production of threenew types of computers, called model X, Y, and Z, respectively. Each type will require assembly time, inspection time, and storage space. The availability of each of these resources is limited. Specifically, available assembly time is 400 hours, available inspection time is 300 hours, and available storage space is 500 cubic feet (about 14.2 ms). The amount of each resource required for the different products is reported in the table below. Model X earns a profit of $100 per unit, model Yearns a profit of $125 per unit, and model 2 earns a profit of $200 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 12 model X computers. In addition, management requires that the fraction of total production made up of model 2 computers must not exceed 25%. RESOURCE REQUIREMENTS Assembly time Inspection time Storage space MODEL hrs/unit hrsJunit cu.…L.P. Model: Maximize Z= 8X+2Y Subject to: 1X+2Y≤6 (C1) 5X+1Y≤20 (C2) X,Y≥0 On the graph on right, the constraints C1 and C2 have been plotted. Using the point drawing tool, plot the four corner points for the feasible area. The optimum solution is: X = (round your response to two decimal places). Y = (round your response to two decimal places). Optimal solution value Z = (round your response to two decimal places).