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: afuel 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 tonof 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 baseproduced.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 Productiona.Material 1Material 2Material 338 tons11 tons39 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel additive and S is the number of tons of solventbase.)Using the graphical solution procedure, find the optimal solution and determine how many tonsof each product should be produced. Using this information, what is the projected total profitcontribution (in dollars)?

First, I would formulate the LP, after the formulation of this LP, I would solve this optimization…

Answered: a. Using the graphical solution…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...

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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.
Slim-Down Manufacturing makes a line of nutritionally complete, weight-reduction beverages. One of their products is a strawberry shake which is designed to be a complete meal. The strawberry shake consists of several ingredients. Some information about each of these ingredients is given below. Calories Total Vitamin Calories Content (per tbsp) (mg/tbsp) 50 20 100 0 120 80 Ingredient Strawberry flavoring Cream Vitamin supplement Artificial sweetener Thickening agent from fat (per tbsp) 1 75 0 0 30 0 50 0 2 Thickeners (mg/tbsp) 3 8 1 2 25 Cost (c/tbsp) 10 8 25 15 6 The nutritional requirements are as follows. The beverage must total between 380 and 420 calories (inclusive). No more than 20% of the total calories should come from fat. There must be at least 50 milligrams (mg) of vitamin content. For taste reasons, there must be at least two tablespoons (tbsp) of strawberry flavoring for each tbsp of artificial sweetener. Finally, to maintain proper thickness, there must be exactly 15 mg…
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a. Using the graphical solution procedure, find the optimal solution and determine how many tons of each product should be produced. Using this information, what is the projected total profit contribution (in dollars)?