The colouring of fabrics can be effected through staining (painting), dyeing or printing. As an expert in textile designing, discuss how a six-yard cotton plain fabric can be coloured with vat dyes through the use of a resist dyeing technique
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The colouring of fabrics can be effected through staining (painting), dyeing or printing. As an expert in textile designing, discuss how a six-yard cotton plain fabric can be coloured with vat dyes through the use of a resist dyeing technique.
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- Cranberries can be harvested using either a "wet" method or "dry" method. Dry-harvested cranberries can be sold at a premium, while wet harvested cranberries are used mainly for cranberry juice and bring in less revenue. Fresh Made Cranberry Cooperative must decide how much of its cranberry crop should be harvested wet and how much should be dry harvested. Fresh Made has 6000 barrels of cranberries that can be harvested using either the wet or dry method. Dry cranberries are sold for $32.50 per barrel and wet cranberries are sold for $18.50 per barrel. Once harvested, cranberries must go through dechaffing and cleaning operations. The dechaffing and the cleaning operations can each be run 24 hours per day for the seasons about 6 weeks long (for a total of 1,008 hours). Each barrel of dry cranberries requires 0.20 hours in the dechaffing operation and 0.33 hours in the cleaning operation. Wet cranberries require 0.06 hours in the dechaffing operation and 0.13 hours in the cleaning…The Elastic Firm has two products coming on the market, Zigs and Zags. To make a Zig, the firm needs 10 units of product A and 15 units of product B. To make a Zag, they need 20 units of product A and 15 units of product B. There are only 2,000 units of product A and 3,000 units of product B available to the firm. The profit on a Zig is R4 and on a Zag it is R6. Management objectives in order of their priority are: (1) Produce at least 40 Zags. (2) Achieve a target profit of at least R750. (3) Use all of the product A available. (4) Use all of the product B available. (5) Avoid the requirement for more product A. Formulate this as a goal programming problem.A machine shop manufactures two types of bolts. The bolts require time on each of the three groups of machines, but the time required on each group differs, as shown in the table below. Type I Type IIMachine 1 0.2 min 0.2 minMachine 2 0.6 min 0.2 minMachine 3 0.04 min. 0.08 min Production schedules are made up one day at a time. In a day, 300, 720, and 100 minutes are available, respectively, on these machines. Type I bolts sell for 15¢ and type II bolts for 20¢. (a) How many of each type of bolt should be manufactured per day to maximize revenue?(b) What is the maximum revenue?(c) Suppose the selling price of type I bolts began to increase. Beyond what amount would this price have to increase before a different number of each type of bolts should be produced to maximize revenue?
- A Garment Company manufactures blue jeans. Three designs are considered: A, B, and C. The manufacture of design A requires 5 minutes machine time, 20 minutes labor and costs P325. Design B requires 8 minutes machine time, 30 minutes labor and costs P350 to produce. Finally, design C, the top of the line requires 10 minutes machine time, 1 labor hour, and costs P425 to produce. Brand A sells for P650, brand B for P750, and brand C for P875. The company works on a weekly schedule of five days, with two shifts of 7.5 hours (net time) each. It has six machines available for production and 36 workers on each shift. Its weekly manufacturing budget is P1,750,000. Based on previous demand, they can sell at least 500 units of design B and minimum of 200 units of brand C. Formulate the complete LP model.Creative sports design (CSD) manufactures a standard size racket and an over sized racket. The firm's rackets are extremely light due to the use of a magnesium- graphite alloy that was invented by the firm's founder. Each standard size racket uses 0.125 kilograms of the alloy and each oversize racket uses 0.4 kilograms; over the next two week production period only 80 kilograms of the alloy are available. Each standard size racket uses 10 min. of manufacturing timeand each oversize racket uses 12 min. The profit contributions are $10 for each standard size racket and $15 for each oversized racket, and 40 hours of manufacturing time are available each week. Managment specified that at least 20% of the total production must3 be the standard size racket. How many rackets of each type should CSD manufacture over the next 2 weeks to maximize the total profit contributions? Assume that because of the unique nature of their products, CSD can sell as many rackets as they can produce?Sales representatives sell two products A and B. Based on historical data there is an average 20 euro commission for every call on product A and a 10 euro commission for every call on product B. Data also shows that sales representatives spend about 3 hours per call for product A and 2 hour for product B. The company requires at least 25 calls per month for each product and not more than 100 calls per month on any one product. How should the sales representatives allocate their monthly 165 working hours between making calls selling products A and B if they want to maximize their commission? a) Mathematically formulate the LP model for maximizing commissions (=primal problem) b) Mathematically formulate the dual problem of the primal problem. Implement both LP models (primal and dual) using Excel Solver. c) Report the optimal objective functions, decision variable values and the shadow prices of both the primal and dual problems. d) Confirm that these numbers are in line with…
- FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below. Ingredient Cost Volume Fat Grams Calories Dried fruit 0.35 0.25 cup 0 150 Nut mix 0.50 0.375 cup 10 400 Cereal mix 0.20 1 cup 1 50 Let D = number of ounces of dried fruit mix in the blend; N = number of ounces of nut mix in the blend ; C = number of ounces of cereal mix in the blend. The constraint that would ensure the mixture has no more than 25 grams of fat is:Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.Green Vehicle Inc. manufactures electric cars and small delivery trucks. It has just opened a new factory where the C1 car and the T1 truck can both be manufactured. To make either vehicle, processing in the assembly shop and in the paint shop are required. It takes 1/40 of a day and 1/60 of a day to paint a truck of type T1 and a car of type C1 in the paint shop, respectively. It takes 1/50 of a day to assemble either type of vehicle in the assembly shop. A T1 truck and a C1 car yield profits of $300 and $220, respectively, per vehicle sold. a) Define the objective function and constraint equations. b) Graph the feasible region. c) What is a maximum-profit daily production plan at the new factory? d) How much profit will such a plan yield, assuming whatever is produced is sold?
- Sunseel Industries produces two types of raw materials, A and B, with a production cost of $4 and $8 per unit, respectively. The combined production of A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 production hours are available per month. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost.A machine part to be fabricated may be made from alloy of either of two metals. There is an order for 10,000 units. Metal A costs 3 pesos per kg, while Metal B costs 9 pesos per kg. If Metal A is used, the material per unit weighs 110 grams; for metal B, 30 grams. When metal A is used, 50 units can be produced per hour; for metal B, 80 units per hour. Metal B fabrication requires the aid of a tool costing P1,000, which will be useless after the 10,000 units are finished. The machine operator's wage is P50 per hour. If all other costs are identical, determine which material will be more economical to finish the 10,000-unit order. How much is the total cost difference between the use of metal A and metal B?THE PRIMER INC. Primer Inc. offers plumbing and air conditioning services to customers in Kumasi, Ghana. The company’s product strategy is to solve the customer’s problem irrespective of what it takes, at the time the customer needs it solved. The company provides same day service for customers, and the aim is to make the customer happy before leaving. The services of the company are available 24 hours a day, 7 days a week for customers. There is no extra charge for requests made on holidays, odd hours of the day, or in festive seasons. The company aims to be available at the call of customers without charging a pesewa extra, even at times when rival firms won’t get out of bed. The company fixes the price of the service before it begins, and customers can be assured of no extra charges. Irrespective of the customer’s location in the city, Primer Inc. does not charge additional fees for transportation. For all services, the company provides a one year guarantee on all parts and labour…