3,000 3,000 The marketing department of the company forecasts a demand of 80,000 bottles of A, 22,000 bottles of B and 40,000 bottles of C during the month of June. The operating costs per day of plants at T1 and T2 are Rs. 6,000 and Rs. 4,000 respectively. Find (graphically) the number of days for which each plant must be run in June so as to minimize the operating costs while meeting the market demand.
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- Amy Zeng, owner ofZeng's Restaurant Distributions,supplies nonperishable goods to restaurants around the metroarea. She stores all the goods in a storage area with a single dockand one aisle. The goods are divided into five categories accordingto the following table. The table indicates the number of tripsper month to store or retrieve items in each category, as well asthe number of storage blocks taken up by each. The following picture of the storage area provides an identificationnumber for each of the 16 storage blocks. For each item category,indicate into which blocks it should be stored.1. Maribel is selling regular and special juices. To make a bottle of regularjuice, she needs 2 pounds of mango and 3 pounds of pineapple. On theother hand, 4 pounds of mango and 2 pounds of pineapple are needed tomake a bottle of special juice. A profit of P30 is made for a bottle of regularjuice and P40 for a bottle of special juice. Maribel is currently has 800pounds of mango and 480 pounds of pineapple. She wants to make at least180 bottles of special juice. How many bottles of each type of juice mustshe make to maximize her profit? How much will be her maximum profit? 2. A calculator company produces a scientific calculator and a graphingcalculator. Long-term projections indicate an expected demand of atleast 100 scientific and 80 graphing calculators each day. Because oflimitations on production capacity, no more than 200 scientificand 170 graphing calculators can be made daily. To satisfy a shippingcontract, a total of at least 200 calculators much be shipped each day. Ifeach…Gerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements are Day M T W Th F S Su Requirements 7 3 4 4 5 4 5 Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have 2 consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S-Su pair in case of a tie. (Note: If there is a tie that cannot be broken by following the preference to the S-Su pair, choose the pair closest to the beginning of the considered week.) The minimum number of workers is 7 workers. (Enter your response as a whole number.) Specify the workforce schedule for each employee by indicating the day offs (other days are considered to be…
- Gerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements are Day M T W Th F S Su Requirements 7 3 5 5 6 2 2 Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have 2 consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S-Su pair in case of a tie. (Note: If there is a tie that cannot be broken by following the preference to the S-Su pair, choose the pair closest to the beginning of the considered week.) Part 2 The minimum number of workers is _________workers. (Enter your response as a…Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $95, and $133, respectively. The production requirements per unit are as follows: Number ofFans Number ofCooling Coils ManufacturingTime (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 300 fan motors, 340 cooling coils, and 2000 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 67E + 95S + 133D s.t. 1E + 1S + 1D ≤ 300 Fan motors 1E + 2S + 4D ≤ 340 Cooling coils 8E + 12S + 14D ≤ 2000 Manufacturing time E, S, D ≥ 0 The computer solution is shown in the figure below. Optimal Objective Value = 17380.00000 Variable Value…A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?b. What is the maximum price the store would be justified in paying for additional pine bark?c. What is the marginal value of labor? Over what range is this value in effect?d. The manager obtained additional machine time through better scheduling. How much additional machine time can be effectively used for this operation? Why?e. If the manager can obtain either additional pine bark or additional storage space, which oneshould she choose and how much (assuming…
- A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2),and chips (x3). The process requires pine bark, machine time, labor time, and storage space. Thefollowing model has been developed.Maximize Z = 9 x1 + 9x2 + 6x3 (profit)Subject toBark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutesLabor 2x1 + 4x2 + 3x3 ≤ 480 hoursStorage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 a. What is the marginal value of a pound of pine bark? Over what range is this price valueappropriate?The admissions office at State University wants to de-velop a planning model for next year’s entering freshman class. The university has 4500 available openings forfreshman. Tuition is $8600 for an in-state student and$19,200 for an out-of-state student. The university wantsto maximize the money it receives from tuition, but bystate mandate it can admit no more than 47% out-of-statestudents. Also, each college in the university must have atleast 30% in-state students in its freshman class. In orderto be ranked in several national magazines, it wants thefreshman class to have an average SAT score of 1150.Following are the average SAT scores for last year’sfreshman class for in-state and out-of-state students ineach college in the university, plus the maximum size ofthe freshman class for each college. a. Formulate and solve a linear programming model thatwill determine the number of in-state and out-of-statestudents that should enter each college. b. If the solution in part (a) does not…The Gulf Coast Foundry is developing a long-range strategic plan for buying scrap metal for its foundry operations. The foundry can buy scrap metal in unlimited quantities from two sources, Atlanta (A) and Birmingham (B), and it receives the scrap daily in railroad cars. The scrap is melted down, and lead and copper are extracted for use in the foundry processes. Each railroad car of scrap from source A yields 1 ton of copper and 1 ton of lead and costs $10,000. Each railroad car of scrap from source B yields 1 ton of copper and 2 tons of lead and costs $15,000. If the foundry needs at least 21/2 tons of copper and at least 4 tons of lead per day for the foreseeable future, how many railroad cars of scrap should be purchased per day from Source A and Source B to minimize the long-range scrap metal cost?
- A company has three plants at location A,B and C which produce the same product. It has to supply this to buyers located at P, Q and R. The weekly plant capacities for A, B and C are 250, 800 and 350 units respectively, while the buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit shipping cost (in Ksh) are given as Plant Buyer P Buyer Q Buyer R A 8 4 10 B 9 7 9 C 6 5 8 Determine the distribution for the company so as to minimize the cost of transportation using least cost method.Riesemberg Medical Devices is allocating next year's budget among its divisions. As a result, the R&D Division needs to determine which R&D projects to fund. Each project requires various software and hardware and consulting expenses, along with internal human resources. A budget allocation of $1,300,000 has been approved, and 35 engineers are available to work on the projects. The R&D group has determined that at most one of projects 11 and 77 should be pursued, and that if project 66 is chosen, then project 11 must also be chosen. Develop a model to select the best projects within the budget.Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rod is $2,000, and the cost required to set up the production for the 6-cylinder connecting rod is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line.Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Letx4 = the number of 4-cylinder connecting rods produced next week,x6 = the number of 6-cylinder connecting rods produced next week,s4 = 1 if the production line is set up to produce the 4-cylinder…