38. A company manufactures a mechanical device which consists of four parts, each of which can beproduced in three different departments. Table 3 shows the production rates (per hour) for the fourparts in each of the four departments. The departments (1,2,3) have limited capacities of 240, 320,and 170 hours, respectively.Department123Part 181321TABLE 3Production rate (no. /hour)Part 212119Part 37812Part 451415The company wants to determine the number of hours of each department which should be assignedto each part in order to maximize the number of complete mechanical devices.Formulate the problem as a linear programming model.

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Answered: A company manufactures a mechanical…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.4: Fixed-cost Models

Problem 13P

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2. A firm makes two products X and Y and has a total production capacity of 9 tons per day.X and Y requiring the same production capacity. The same has a permanent contract to supply at least two tons of X and at least 3 tons of Y per day to another company. Each ton of X requires 20 machine hours of production time and each ton of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The entire firm's output can be sold and profit made is 80 R.O of X and 120 R.O per ton of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. Formulate a LPP.
1. A distillery produces two types of alcohol for filling and distributing, the regular beer and the premium beer. A batch of regular costs $375 to manufacture and a container of the Premium beer costs $420. The manufacturer wishes to establish the weekly production plan that minimizes cost. Production of these products is limited to processing, testing and material. Each batch of regular beer requires 4 hours processing whereas each batch of premium requires 2 hours of processing. Further each batch of regular requires 4 hours of testing compared to 6 hours of testing for a batch of Super. A batch of regular and a batch of Super each require 1 litre of material. Processing and testing have a maximum of 100 and 180 hours available and the total material available is 40 litres. Because of an agreement, the sales of regular beer are limited to a weekly maximum of 20 batches and to honour an agreement with a loyal distributor, at least 10 batches of premium beer must be sold each week.…
1.A clockmaker makes two types of woodenclocksto sell at various malls. It takes him three hours to assemble a pine clock, which requires two oz of varnish. It takes four hours to assemblea molave clock, which takes four oz of varnish. He has eight oz of varnish available in stock and can work 12 hours. If he makes a P100 profit on each pine clock and P120 on each molave clock, how many of each type should he make to maximize his profit?2.A biologist is developing two new strains of bacteria. Each sample of Type A bacteria produces five new viable bacteria,and each Type B bacteria produces six new viable bacteria. Altogether, at least 150 new viable bacteria must be produced. At least 10, but not more than 20,of the original sample,must be Type A,and not more than 60 of the samples must be Type B. A sample of Type A costs P500,and a sample of Type B costs P700. If both types are to be used, how many samples of each type should be used to minimize the cost?
A company must meet (on time) the following demands:quarter 1—30 units; quarter 2—20 units; quarter 3—40units. Each quarter, up to 27 units can be produced withregular-time labor, at a cost of $40 per unit. During eachquarter, an unlimited number of units can be produced withovertime labor, at a cost of $60 per unit. Of all unitsproduced, 20% are unsuitable and cannot be used to meetdemand. Also, at the end of each quarter, 10% of all unitson hand spoil and cannot be used to meet any futuredemands. After each quarter’s demand is satisfied andspoilage is accounted for, a cost of $15 per unit is assessedagainst the quarter’s ending inventory. Formulate an LP thatcan be used to minimize the total cost of meeting the nextthree quarters’ demands. Assume that 20 usable units areavailable at the beginning of quarter 1.
The manager of the deli section of a grocery superstore has just learned that the department has112 pounds of mayonnaise, of which 70 pounds is approaching its expiration date and must beused. To use up the mayonnaise, the manager has decided to prepare two items: a ham spread anda deli spread. Each pan of the ham spread will require 1.4 pounds of mayonnaise, and each panof the deli spread will require 1.0 pound. The manager has received an order for 10 pans of hamspread and 8 pans of the deli spread. In addition, the manager has decided to have at least 10 pansof each spread available for sale. Both spreads will cost $3 per pan to make, but ham spread sellsfor $5 per pan and deli spread sells for $7 per pan.a. Determine the solution that will minimize cost.b. Determine the solution that will maximize profit.
A manufacturing process has 12 workers and 6 stations. The process iscompleted in the order given below. Where there are multiple workers within a station,each worker works independently on his/her own unit. Assume inventory buffers areallowed between each station.Station Staffing Processing time (hoursper unit per worker)A 2 2.20B 1 1.25C 3 2.00D 2 2.60E 3 3.00F 1 0.75What is the maximum number of units per hour that can be produced? Assume they startthe day with inventory at each station to work on
c. Suppose that 10, 6, and 8 hours of overtime may be scheduled in departments A, B, andC, respectively. The cost per hour of overtime is $18 in department A, $22.50 in departmentB, and $12 in department C. Formulate a linear programming model that canbe used to determine the optimal production quantities if overtime is made available.What are the optimal production quantities, and what is the revised total contributionto profit? How much overtime do you recommend using in each department? What isthe increase in the total contribution to profit if overtime is used?
Please note that this question is different from what you have in your library. This question has 3 variables ie 3 departments. Please help solve the problem. A co markets 2 products which are produced in 3 successive departments. The contribution per unit of the 2 products and the production capacity of the 3 departments are X. Y Contribution. 10. 15 Machining dept (hrs) 3. 4 Foundry dept (hrs) 4 2 Painting dept (hrs) 4 5 A constraint on production is that each dept has a limited number of hours available for the forthcoming plan period as shown below: Department. Available hours Machining. 1'200 Foundry. 1000 Painting. 1300 Required- 1. Formulate the linearr programming problem for the above information. 2. Solve them graphically
Becton Labs, Inc., produces various chemical compounds for industrial use. One compound, called Fludex, is prepared using an elaborate distilling process. The company has developed standard costs for one unit of Fludex, as follows: Standard Quantityor Hours Standard Priceor Rate Standard Cost Direct materials 2.30 ounces $ 26.00 per ounce $ 59.80 Direct labor 0.50 hours $ 14.00 per hour 7.00 Variable manufacturing overhead 0.50 hours $ 3.40 per hour 1.70 Total standard cost per unit $ 68.50 During November, the following activity was recorded related to the production of Fludex: Materials purchased, 12,500 ounces at a cost of $305,625. There was no beginning inventory of materials; however, at the end of the month, 2,800 ounces of material remained in ending inventory. The company employs 21 lab technicians to work on the production of Fludex. During November, they each worked an average of 150 hours at an average pay rate of $12.00 per hour.…
You are given a linear programming problem. Maximize P = 6x + 4y subject to 2x + 3y ≤ 12 Resource 1 2x + y ≤ 8 Resource 2 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 + 4y. 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.(e) Identify the binding and nonbinding constraints. constraint 1 constraint 2
A paper-recycling plant processes box board, tissuepaper, newsprint, and book paper into pulp that can be usedto produce three grades of recycled paper (grades 1, 2, and3). The prices per ton and the pulp contents of the fourinputs are shown in Table 82. Two methods, de-inking andasphalt dispersion, can be used to process the four inputsinto pulp. It costs $20 to de-ink a ton of any input. Theprocess of de-inking removes 10% of the input’s pulp,leaving 90% of the original pulp. It costs $15 to applyasphalt dispersion to a ton of material. The asphalt dispersionprocess removes 20% of the input’s pulp. At most, 3,000tons of input can be run through the asphalt dispersionprocess or the de-inking process. Grade 1 paper can only beproduced with newsprint or book paper pulp; grade 2 paper,only with book paper, tissue paper, or box board pulp; andgrade 3 paper, only with newsprint, tissue paper, or boxboard pulp. To meet its current demands, the company needs500 tons of pulp for grade 1…
3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds

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