"Using an optimization model, a company wants to determine the most efficient way to allocate its resources to maximize profits. The company produces multiple products that require different amounts of raw materials, labor, and machine time. The production process has multiple constraints and the company wants to ensure that it meets customer demand while minimizing costs. Analyze the company's production process, formulate an optimization model, and recommend the optimal resource allocation strategy to maximize profits.
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"Using an optimization model, a company wants to determine the most efficient way to allocate its resources to maximize profits. The company produces multiple products that require different amounts of raw materials, labor, and machine time. The production process has multiple constraints and the company wants to ensure that it meets customer demand while minimizing costs. Analyze the company's production process, formulate an optimization model, and recommend the optimal resource allocation strategy to maximize profits.
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- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)An Insurance Company is introducing two new product lines: special risk insuranceand mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit onmortgages. Management wishes to establish sales quotas for the new product lines tomaximize total expected profit. Please see figure for work requirements. The sensitivity report for this optimization problem is given in the following figure 1 - Can you determine the optimal value (maximum expected profit) based on the sensitivityreport? 2 - Identify the non-binding constraint(s).
- Tomato growers in the Netherlands have a huge productivity advantage over their competitors in Italy and Greece. Although those countries are sun drenched while the Netherlands are anything but, computerized, climate-controlled greenhouses, and a "soil" spun from basalt and chalk that resembles cotton candy, allows for precise control of humidity and nutrition, and enables growers to produce their crops year around. Growers in Italy and Greece generally grow their crops outdoors or in unheated greenhouses, and can only manage two crops a year. Dutch growers are able to achieve yields that are about ten times per square yard of those of Italian and Greek growers. And the Dutch have a supply chain advantage: an integrated Dutch trading company works closely with supermarket chains in Europe and suppliers around the world, so farmers are able to sell their output in high volume, rather than locally the way many farmers in other countries do. That enables Dutch growers to more closely…Describe a practical optimization problem, establish its optimization model, and give the solution ideaHow is duality used to transform optimization problems in various domains, such as economics or finance?
- Explain the term “Constrained Optimization” as Thaler used in the first chapter of Misbehaving.An Insurance Company is introducing two new product lines: special risk insuranceand mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit onmortgages. Management wishes to establish sales quotas for the new product lines tomaximize total expected profit. Please see figure for work requirements(a) Formulate a linear programming model for this problem.MacDonald opens an 800 acre farm to raise wheat, beef, and alfalfa. He is planning his activities for the next year. Profit contribution from raising and selling wheat is $120/acre; profit contribution from raising and selling beef is $450/ton; alfalfa costs $7/ton to raise and sells for $22/ton. It takes 5 tons of alfalfa to raise 1 ton of beef. Alfalfa can also be bought in the market for $28/ton. The land and water requirements for wheat, beef and alfalfa, and the total availability of land and water are shown in the table below. What decisions should MacDonald take to maximize his total profit? Solve this problem using the Excel solver.
- The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability: Labor-Hours Required(hours/unit) Department Product 1 Product 2 Hours Available A 1.00 0.35 100 B 0.30 0.20 38 C 0.20 0.50 50 Profit contribution/unit $30.00 $15.00 (a) Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products 1 and 2. If required, round your answer to two decimal places. Product 1 Product 2 Production (b) In computing the profit contribution per unit, management does not deduct labor costs because they are considered fixed for the upcoming planning period. However, suppose that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling…The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability: Labor-Hours Required(hours/unit) Department Product 1 Product 2 Hours Available A 1.00 0.35 95 B 0.30 0.20 38 C 0.20 0.50 50 Profit contribution/unit $30.00 $15.00 (a) Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products 1 and 2. If required, round your answer to two decimal places. Product 1 Product 2 Production (b) In computing the profit contribution per unit, management does not deduct labor costs because they are considered fixed for the upcoming planning period. However, suppose that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for…WhAt is Integer Linear Optimization and how it is solved?