SAMCIS Chemicals produces two products that are sold as raw materials tocompanies manufacturing bath soaps and laundry detergents. Based on an analysisof current inventory levels and potential demands for the coming month, SAMCISmanagement specified that the combined production for products A and B musttotal to at least 350 gallons. Separately, a major customer's order of 125 gallons ofproduct A must also be satisfied. Product A requires 2 hours of processing time pergallon and product B requires 1 hour of processing time per gallon. For the comingmonth, 600 hours of processing time are available. SAMCIS's objective is to satisfythese requirements at a minimum total production cost. Production costs are $2 pergallon for product A and $3 per gallon for product B. Generate the mathematicalmodel for the optimal number of product A and B to be produced by SAMCISchemicals.

Given that SAMCIS Chemicals produces two products that are sold as raw materials to companies…

Answered: SAMCIS Chemicals produces two products…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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need comprehensive and correct answers.This question is about optimization.
Protective Research, Inc. received an order to produce a specially designed fence for preventing automobile accidents on the highways. The fence is manufactured in two sections, each requiring no more than 9 units of material A and no more than 6 units of material B. While each unit of material A weighs 4 kgs and B weighs 6 kgs, the final product must weigh exactly 48 kgs. Management figures profit in terms of input units, $240 per unit from material A and $160 from material B. What is the profitable mix.
Ethan Steel, Inc. has three factories that manufacture steel components for three different rail projects located at three different sites. They want to determine how many steel components must be transported from each factory to each project site. The demand for the steel components for the three projects, A, B and C, are 2500, 3000 and 4500, respectively. The production and shipping details are as below: Production details: Factory Maximum capacity 1 3000 5000 3000 2 3 Shipping details (with per-unit shipping cost in dollars): Project Factory A B C 1 7 8 2 2 6 5 4 3 1 9 6 Develop a linear programming optimization model to determine the distribution plan (from factories to projects) that minimizes the total transportation cost. (Do NOT solve the model.)
The monthly demand for Williams Tchotchkes (q measured in 1000s of tchotchkes) depends on the price that they set for their tchotchkes (p measured in dollars), the average price of substitutes for their tchotchkes (p, also measured in dollars), and the average monthly disposable income in the market for tchotchkes (y measured in $1000s). The current prices are p = $10 and p₁ = $11, the current monthly demand for Williams Tchotchkes is 8000 tchotchkes and the current average monthly disposable income in the tchotchkes market is $3500. Furthermore, it is known that Əq Op p=10 Pg=11 y=3.5 = -0.31, Əq aps P=10 Pg=11 y=3.5 = 0.44 and Əq dy p=10 Pg=11 y=3.5 = 0.72. Scenario 1: Suppose that p increases by $0.20, p, increases by $0.35 (from their current values), and income doesn't change. In this scenario, monthly demand for Williams Tchotchkes' monthly will [Select] , and Williams Tchotchkes' monthly revenue will [Select] Scenario 2: Now (instead) suppose that average monthly income in the…
A producer of high end exercise equipment operates 6 hours per day, 350 days per year, and has a demand of 300 units per day. Assume a kanban container size of 8 units. Workstation times are as follows: - average wait time is 2 minutes - average handling time is 4 minutes - average processing time is 5 minutes. In addition, management has established a safety stock policy of 150 seconds. How many kanbans should be placed in front of this workstation? Please round up to a whole number, no decimals.
Trans Global Tractor Trailers has decided to spend up to $2,700,000 on a fleet of new trucks, and it is considering three models: the Gigahaul, which has a capacity of 6,000 cubic feet and is priced at $60,000; the Megahaul, with a capacity of 5,000 cubic feet, priced at $50,000; and the Picohaul, with a capacity of 2,000 cubic feet, priced at $40,000. The anticipated annual revenues are $500,000 for each new truck purchased (regardless of size). Trans Global would like a total capacity of up to 234,000 cubic feet and feels that it cannot provide drivers and maintenance for more than 54 trucks.How many of each should it purchase to maximize annual revenue? (Gigahaul, Megahaul, Picohaul) = trucks What is the largest possible revenue it can make? $
The company has data on demand and factory capacity for the next 4 months as in the table. Unit cost with regular time $ 24, overtime cost $ 28, on subcontract $ 34. Storage costs $ 2 per unit per month; backorders cost $ 5 per unit per month. Initial inventory is as many as 120 units, and it is expected that by the end of July there will be an inventory of 100 units. April May June July Demand 460 450 480 480 Regular Capacity 370 370 380 380 Overtime Capacity 60 60 60 60 Subcontract Capacity 30 30 30 30 Use the transportation method to optimize the aggregate plan. Determine the production cost each month and the total cost for 4 months
1. ARI Chemicals produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demands for the coming month, ARI management specified that the combined production for products A and B must total at least 350 gallons. Separately, a major customer’s order of 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon and product B requires 1 hour of processing time per gallon. For the coming month, 600 hours of processing time are available. ARI's objective is to satisfy these requirements at a minimum total production cost. Production costs are $2 per gallon for product A and $3 per gallon for product B. - Generate the mathematical model for the optimal number of products A and B to be produced by ARI chemicals. - Create Graph
Johnson Industries received a contract to develop and produce four high-intensity longdistance receiver/transmitters for cellular telephones. The i rst took 2,000 labor hours and $39,000 worth of purchased and manufactured parts; the second took 1,500 labor hours and $37,050 in parts; the third took 1,450 labor hours and $31,000 in parts; and the fourth took 1,275 labor hours and $31,492 in parts.Johnson was asked to bid on a follow-on contract for another dozen receiver/transmitter units. Ignoring any forgetting factor effects, what should Johnson estimate time and parts costs to be for the dozen units? (Hint: There are two learning curves—one for labor and one for parts.)
Find the total cost of the following shipment of materials: 23 floor boxes listed at $4.00 each, less 15% ; 150 half-inch conduits listed at $0.60 each, less 20% ; 125 convenience outlets listed at $0.79 each, less 10% ; 83 single-pole flush switches listed at $0.45 each, less 30%.
A company uses four special tank trucks to deliver four different gasoline products to customers. Eachtank has five compartments with capacities: 500, 750, 1200, 1500, and 1750 gallons. The daily demands forthe four products are 10000, 15000, 12000, and 8000 gallons. Any quantities that cannot be delivered by thecompany’s four trucks must be subcontracted at the additional costs of 5, 12, 8, and 10 cents per gallon forproducts 1, 2, 3, and 4, respectively. The goal is to develop the optimal daily loading schedule for the fourtrucks that will minimize the additional cost of subcontracting. Formulate this problem as an integer linearprogram, and solve it using linear program solver.
A florist provides fresh flowers to shops in Wollongong. At present she has one nursery in Goulburn with capacity 9000 units a year. The florist is considering opening shops in Canberra and Sydney, and has found three potential nursery sites at Wagga, Orange and Bathurst. The transportation tableau below summarises the projected nursery capacities (units), the cost per unit of shipping from each nursery to each destination (dollars), and the demand (units) for the coming year. j=1 j=2 j=3 Sydney Capacities Wollongong Canberral 5 i=1 Goulburn 12 9000 i=2 Wagga 7 10 4000 i=3 Orange 4 7000 i=4 Bathurst 11000 Demand 11000 5000 8000 There are further constraints on how the nurseries can be located: • If a nursery is located in Wagga, another must be located in Bathurst and vice- versa. • One nursery can be located in Orange or Bathurst, but not both. Suppose that the costs of establishing new nurseries are Wagga $180,000 Orange $160,000 Bathurst $270,000 The goal is to develop a 0-1…

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