Describe the usage of iso cost line in the graphical minimisation problem of linear programming ?
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Describe the usage of iso cost line in the graphical minimisation problem of linear programming ?
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.I need a detailed explanation and assistance to solve this problem: Wineco produces wine cooler as a blend of wine, grape juice and apple juice ingredients, which it sells for $4 per gallon. The costs of ingredients are given in the following table: Cooler Ingredient Price per Gallon ($) wines 1.20 grape juice 1.40 Apple juice 0.60 Wineco owns a blending plant with a production capacity of 200 gallons per day. Because the plant is fully automated, all other production costs are negligible by comparison to the cost of ingredients, and can be ignored. Government regulations mandate that wine cooler products must satisfy the following guidelines: At least 10% of the blend produced must be grape juice. The ratio of apple juice to grape juice in the blend produced must be 2.5:1 The blend produced must contain between 20% and 25% wine. Wineco wishes to use LP in order to determine the quantities of ingredients to buy for a day’s production of wine cooler, so…The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend? Type A Type B Shade Tolerance 1 1 Traffic Resistance 2 1 Drought Resistance 2 5 Formulate a LP Model for this problem.
- Western Chassis produces high-quality polished steel and aluminum sheeting and two lines of industrial chassis for the rack mounting of Internet routers, modems, and other telecommunications equipment. The contribution margin (contribution toward profit) for steel sheeting is $0.40 per pound and for aluminum sheeting is $0.60 per pound. Western earns $12 contribution on the sale of a Standard chassis rack and $15 contribution on a Deluxe chassis rack. During the next production cycle, Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or in chassis. Similarly, 20,400 pounds of aluminum are available. One standard chassis rack requires 16 pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12 pounds of each metal. The output of metal sheeting is restricted only by the capacity of the polisher. For the next production cycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. Chassis manufacture…ProHaul specializes in trans-American shipments for businesses through the delivery of containers. For every container the company loads on its trucks, ProHaul estimates the haul costs $1,000. In addition, containers are weighed and for each pound, there are hauling fees of $0.15. ProHaul plans to charge $0.49 per pound to his customers.How many pounds would a container have to hold in order for the company to Break Even?Western Chassis produces high-quality polished steel and aluminum sheeting and two lines ofindustrial chassis for the rack mounting of Internet routers, modems, and other telecommunicationsequipment. The contribution margin (contribution toward profit) for steel sheeting is $0.40 per poundand for aluminum sheeting is $0.60 per pound. Western earns $12 contribution on the sale of aStandard chassis rack and $15 contribution on a Deluxe chassis rack. During the next productioncycle, Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or inchassis. Similarly, 20,400 pounds of aluminum are available. One standard chassis rack requires 16pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12 pounds of each metal.The output of metal sheeting is restricted only by the capacity of the polisher. For the next productioncycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. Chassismanufacture can be…
- Travel Co. specializes in trans-American moves for businesses and individuals through the shipment of containers. For every container the company transports via rail, Travel Co. must pay the rail owners $5,000. In addition, containers are weighed and for each pound of weight, the company must pay $0.40. Harry plans to charge $0.68 per pound to his customers. How many pounds would a container have to hold in order for the company to Break Even? What would the total revenue be at Break Even? The company finds out that to maintain the integrity of its containers, each container could only hold an average of 16,000 pounds. What would the company have to charge customers to make $7,000 in profit on each container?Dr. Thompson makes three bean mixes for coffee shops located in the Austin. The three mixes, referred to as the Tameka Mix, the Christian Mix, and the Tamia Mix, are made by mixing different percentages of five types of beans. In preparation for the fall season, Dr. Thompson just purchased the following shipments of beans at the prices shown: Type of Beans Shipment Amount in pounds Cost Per Shipment in dollars Arabica 6000 7500 Robusta 7500 7125 Liberica 7500 6750 Excelsa 6000 7200 Juno 7500 7875 The Tameka Mix consists of 15% Arabica, 25% Robusta beans, 25% Liberica, 10% Excelsa, and 25% Juno. The Christian Mix consists of 20% of each type of beans, and the Tamia Mix consists of 25% Arabica, 15% Robusta beans, 15% Liberica, 25% Excelsa, and 20% Juno. Dr. Thompson analyzed the cost to get the beans ready and determined that the profit contribution per pound is $1.65 for the Tameka Mix, $2.00 for the Christian Mix, and $2.25 for the…Dr. Thompson makes three bean mixes for coffee shops located in the Austin. The three mixes, referred to as the Tameka Mix, the Christian Mix, and the Tamia Mix, are made by mixing different percentages of five types of beans. In preparation for the fall season, Dr. Thompson just purchased the following shipments of beans at the prices shown: Type of Beans Shipment Amount in pounds Cost Per Shipment in dollars Arabica 6000 7500 Robusta 7500 7125 Liberica 7500 6750 Excelsa 6000 7200 Juno 7500 7875 The Tameka Mix consists of 15% Arabica, 25% Robusta beans, 25% Liberica, 10% Excelsa, and 25% Juno. The Christian Mix consists of 20% of each type of beans, and the Tamia Mix consists of 25% Arabica, 15% Robusta beans, 15% Liberica, 25% Excelsa, and 20% Juno. Dr. Thompson analyzed the cost to get the beans ready and determined that the profit contribution per pound is $1.65 for the Tameka Mix, $2.00 for the Christian Mix, and $2.25 for the…
- VITRAN Bus Services purchases diesel fuel from Domino Gas Supply. In addition to fuel cost, Domino Gas Supply charges VITRAN Bus Services $250 per order to cover the expenses of delivering and transferring the fuel to VITRAN Bus Services storage tanks. The lead time for new shipment from Domino Gas Supply is 10 days, the cost of holding a gallon of fuel in the storage tanks is $0.04 per month, or $0.48 per year and the annual usage of fuel is 150,000 gallons. VITRAN Bus Services buses operate 300 days a year. What is the optimal order quantity for VITRAN Bus Services? How frequently should VITRAN Bus Services order to replenish the gasoline supply?An engineer at Fertilizer Company has synthesized a sensational new fertilizer made of just two interchangeable basic raw materials. The company wants to take advantage of this opportunity and produce as much as possible of the new fertilizer. The company currently has $40,000 to buy raw materials at a unit price of $8000 and $5000 per unit, respectively. When amounts x1 and x2 of the basic raw materials are combined, a quantity q of fertilizer results given by: q = 4x1 + 2x2 - 0.5x12 - 0.25x22 Part A: Formulate as a constrained nonlinear program. Clearly indicate the variables, objective function, and constraints. Part B: Solve the Program with Excel Solver (provide exact values for all variables and the optimal objective function).Bright Furnitures produces chairs and tables that go through M1 and M2. Making a 1 table and 1 chair takes the following time in hours: TABLE CHAIR M1 7 4 M2 5 5 Total of 200 hours are available on M1 and 400 hours on M2. Profit contribution from the sale of a chair is P300 and from a table is P400. Requirement: Determine the optimal mix of tables and chairs so as to maximize the contribution. Use Excel Solver.