A department supervisor is considering purchasing one of two comparable photocopy machines, A or B. Machine A costs $10,000 and Machine B costs $1I0,500.This department replaces photocopy ma- chines every three years. The repair contract for Machine A costs $50 per month and covers an un- limited number of repairs. he repair contract for Machine B costs $200 per repair. Based on past performance, the distribution of the numbe of repairs needed over any one-year period for Machine B is shown below. 5. Number of Repairs Probability 0.50 0.25 0.15 0.10 + 0.25 + 0.35 You are asked to give a recommendation based on overall cost as to which machine, A or B, along with its repair contract, should be purchased. What would your recommendation be? Give statistical justification to support you recommendation. A: 4 10,00 0 B: #1D, S00 right anyher isB simce otsllo10
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- 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…Problem 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.…The Johnny Ho Manufacturing Company inColumbus, Ohio, is putting out four new electronic components. Each of Ho’s four plants has the capacity to add one more prod-uct to its current line of electronic parts. The unit-manufacturing costs for producing the different parts at the four plants areshown in the accompanying table. How should Ho assign the newproducts to the plants to minimize manufacturing costs?ELECTRONICCOMPONENT PLANT123 4C53 $0.10 $0.12 $0.13 $0.11C81 0.05 0.06 0.04 0.08D5 0.32 0.40 0.31 0.30D44 0.17 0.14 0.19 0.15
- A young engineer is considering establishing his own small company.An investment of Php 100,000 will be required which must be recovered in 15years . It is estimated that sales will be Php 150,000 per year and thatoperating expenses will be as follows:Material Php 40,000 per yearLabor Php 70,000 per yearOverhead Php 10,000 + 10% of sales/yearSelling expenses Php 5,000/yearThe young engineer will give up his regular job paying Php 150,000 per yearand devote full time to the operation of the business. This will result indecreasing labor by Php 10,000 per year , material cost by Php 7000 peryear, and overhead cost by Php 8000 per year. If the young engineer expectsto earn at least 20% on his capital, should he invest ?Chalimbana university farm is about to hire workers for its production of cabbage in a space of 5 months. as a student of farm management, you decide to increase the labour by 2 units at the first output,1 unit in the second and third output, 16 units in the fourth output and 20 units in the fifth output at each production level. The farm then realizes an output of 10,25, 65,30, and 30 in that period. The farm workers got a wage of k40 per month.a. Calculate the following at different level of output.i. marginal product, (MP) ii marginal revenue product (MRP) iii marginal resource cost (MRC)Accompany makes two products (1&2) each product requires time on two machines (A&B). specification for each product is as follows. Product1 product2 Processing time on Machine A (hrs/unit) 2 2 Processing time on Machine B (hrs/unit) 1 2 Material and labour cost ( ksh/unit) 14 15 Selling price (ksh/unit) 16 18 Maximum possible sale (units) 130 150 The amount of time available on machine A is 360 hours and on machine B is 260 hours. Formulate the linear programme which, when…
- 8-1 (Production problem) Winkler Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. The table on this page contains all relevant information concerning production times per cabinet produced and production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). Owner Bob Winkler would like to determine a product mix to maximize his daily revenue. Cabinet Style Carpentry (Hours/Cabinet) Painting (Hours/Cabinet) Finishing (Hours/Cabinet) Net Revenue/Cabinet ($) French Provincial 3 1.5 0.75 28 Danish Modern 2 1 0.75 25 Department Capacity (Hours) 360 200 125 a) Formulate as an LP problem. b) Solve using an LP software program or…8-1 (Production problem) Winkler Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. The table on this page contains all relevant information concerning production times per cabinet produced and production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). Owner Bob Winkler would like to determine a product mix to maximize his daily revenue. Perform the four steps (i.e., define variables, determine objective function, identify constraints, list the non-negativity statement) and write equations. Use the table in the pictureA chocolate maker has contracted to operate a small candy counter in a fashionable store. To startwith, the selection of offerings will be intentionally limited. The counter will offer a regular mixof candy made up of equal parts of cashews, raisins, caramels, and chocolates, and a deluxe mixthat is one-half cashews and one-half chocolates, which will be sold in one-pound boxes. In addition, the candy counter will offer individual one-pound boxes of cashews, raisins, caramels, andchocolates.A major attraction of the candy counter is that all candies are made fresh at the counter. However, storage space for supplies and ingredients is limited. Bins are available that can hold theamounts shown in the table.IngredientCapacity(pounds per day)Cashews 120Raisins 200Caramels 100Chocolates 160In order to present a good image and to encourage purchases, the counter will make at least 20boxes of each type of product each day. Any leftover boxes at the end of the day will be removedand given to a…
- #1- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements and available resources for each lot of pens are given in the following table: Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 The profit for either model is $1,000 per lot. a) What is the linear programming model for this problem? b) Using Microsoft Excel's Solver, find the optimal solution. How many Fliptop models and how many Tiptop models should be produced? What is the maximum profit? c) Will there be excess capacity in any resource? Use Excel's Solver and run a sensitivity report to answer the following questions. d) Over which range can the objective function coefficient for Fliptop Models change without affecting the original optimal solution? What is this range called? e) What is the shadow price (dual price) for the plastic constraint and how would you interpret it? f) What is the shadow price (dual price)…ou are given a linear programming problem. Maximize P = 3x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1.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…