1. Washimore Meats To Eat (WMTE) produces three types of hot dogs: regular, beef, and all-meat. The hot dogs are made from some or all of the following ingredients: chicken, beef, pork, and a cereal additive. WMTE has the following amounts of each ingredient available on a daily basis. Ingredient Chicken Pounds per Day Cost per Pound $0.20 $0.30 $0.50 $0.05 200 Вeef 300 Pork 150 Cereal Additive 400 Each type of hot dog has certain ingredient specifications, as follows Specifications Selling Price per Pound Туре Regular Beef and pork combined should not exceed 10% of the mix $0.90 Total chicken should be at least 20% of the mix $1.25 $1.75 Beef Not less than 75% beef All-meat No cereal additive Beef and pork combined should not exceed 50% of the mix (a) Formulate a linear programming model to determine the makeup of a batch of each type of hot dog that maximize profits (revenues from sales minus costs). Let xij represent the pounds of ingredient i in a batch of hot dog type j. (A batch is the total of the ingredients used to make a particular hot dog type.) (b) Solve the model in part (a) using Matlab (or other software).
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- XYZ Limited is a clothing wholesaler that sells the name-brand clothing to department stores andboutique dress shops. Figure on Page No 4 describes the credit sales procedures of XYZ Limited.In particular, the Figure describes different business activities of four departments, including (1)Sales Department, (2) Accounting Department, (3) Warehouse/Shipping, and (4) Mailroom.Further, these activities are elaborated below.The sales department received the customer orders by fax and email. You should be aware thatthese sales orders are usually unstandardised sales order (recall our discussion on the revenue Page 3 of 9cycle during the interactive tutorial for week 4). The sales clerk, who works on commission,performs the following tasks:• approves the credit sales,• calculates commission and discounts, and• records the sales in the sales journal from the PC in the sales department.After entering these records, the sales clerk then prepares three documents, including (1) a salesorder, (2)…RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:Raw Material Amount Available for ProductionMaterial 1 20 tonsMaterial 2 5 tonsMaterial 3 21 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following:i. Compute the value of the objective function…RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:Raw Material Amount Available for ProductionMaterial 1 20 tonsMaterial 2 5 tonsMaterial 3 21 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following:a. What is the linear programming model for this…
- Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, 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 220 fan motors, 340 cooling coils, and 2,600 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 63E + 95S + 135D s.t. 1E + 1S + 1D ≤ 220 Fan motors 1E + 2S + 4D ≤ 340 Cooling coils 8E + 12S + 14D ≤ 2,600 Manufacturing time E, S, D ≥ 0 The computer solution is shown below. Optimal Objective Value = 17700.00000…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…Omega Manufacturing makes three products. Each product requires manufacturing oper-ations in three departments: A, B, and C. The labor-hour requirements, by department,are as follows:TABLE 1:Department Product 1 Product 2 Product 3A 0.25 1.00 0.50B 2.50 2.00 1.00C 2.00 1.50 3.00During the next production period, the labor-hours available are 72 in department A, 370in department B, and 450 in department C.The variable cost of producing each product, sales price of each product, and the fixedsetup cost of a production run for each product is given in Table 2.TABLE 2:Product 1 Product 2 Product 3Variable Cost (per unit) $13.50 $12.30 $11.30Setup Cost $610 $420 $530Sales Price (per unit) $31 $25 $28a) Formulate an Integer Programming model to maximize the profit.b) Solve the problem by using Excel Solver. Show the optimal solution and optimal value in your printouts.
- The Westerbeck Company manufactures several models of automatic washers and dryers. The projected requirements over the next year for their washers are shown in the table below: Month & Requirement January - 710 February - 1090 March - 880 April - 690 May - 1400 June - 1130 July - 1550 August - 1020 September - 530 October - 390 November - 980 December - 1210 Current inventory is 140 units. Current capacity is 1,030 units per month. The average salary of production workers is $1,150 per month. Material costs $140/unit. Each production worker accounts for 35 units per month. Overtime is paid at time and a half. Any increase or decrease in the production rate costs $40/unit for tooling, setup, and line changes. This does not apply, however, to overtime. Inventory-holding costs are $30 per unit per month. Lost sales are valued at $70 per unit. Compare the costs of level and chase demand production plans using the Agg Plan – Level and Agg Plan – Chase…Beauty Products makes two styles of hair dryers, the Petite and the Deluxe. It requires 1 hour of labor to make the Petite and 2 hours of labor to make the Deluxe. The materials cost $4 for each Petite and $3 for each Deluxe. The profit is $5 for the Petite and $6 for the Deluxe. The company has 3450 labor-hours available each week and a materials budget of $9275 per week. How many of each dryer should be made each week to maximize profit?The Mystic Coffee Shop blends coffee on the premises forits customers. It sells three basic blends in one-pound bags:Special, Mountain Dark, and Mill Regular. It uses four dif-ferent types of coffee to produce the blends: Brazilian,mocha, Colombian, and mild. The shop used the followingblend recipe requirements:The cost of Brazilian coffee is $2.00 per pound, the cost ofmocha is $2.75 per pound, the cost of Colombian is $2.90per pound, and the cost of mild is $1.70 per pound. Theshop has 110 pounds of Brazilian coffee, 70 pounds ofmocha, 80 pounds of Colombian, and 150 pounds of mildcoffee available per week. The shop wants to know theamount of each blend it should prepare each week in orderto maximize profit.Formulate and solve a linear programming model forthis problem.
- #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)…Bibbins Manufacturing produces softballs and baseballs for youth recreation leagues. Each softball costs $11 to produce and sells for $17 while each baseball costs $10.50 and sells for $15. The material and labour required to produce each item is listed here along with the availability of each resource. Amount required par Amount Resource Softball Baseball Available Leather 5 oz 4 oz 6000 oz Nylon 6 yds 3 yds 5400 yds Core 4 oz 2 oz 4000 oz Labour 2.5 min 2 min 3500 min Stitching 1 min 1 min 1500 min Assessment Tasks: Answer all 2 questions below. Define the objective function and constraints for this case. Graphically show optimal solution and feasible area for the caseA manager wants to know how many units of each product to produce on a daily basis in order toachieve the highest contribution to profit. Production requirements for the products are shown inthe following table.ProductMaterial 1(pounds)Material 2(pounds)Labor(hours)A 2 3 3.2B 1 5 1.5C 6 — 2.0Material 1 costs $5 a pound, material 2 costs $4 a pound, and labor costs $10 an hour. Product Asells for $80 a unit, product B sells for $90 a unit, and product C sells for $70 a unit. Availableresources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.The manager must satisfy certain output requirements: The output of product A should not bemore than one-third of the total number of units produced; the ratio of units of product A to units ofproduct B should be 3 to 2; and there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solve