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A nutritionist is planning a menu that includes foods A and B as its main staples. Suppose that each ounce of food A contains 2 units of protein, 1 unit of iron, and 1 unit of thiamine; each ounce of food B contains 1 unit of protein, 1 unit of iron, and 3 units of thiamine. Suppose that each ounce of A costs P3, while each ounce of B costs P4. The nutritionist wants the meal to provide at least 12 units of protein, at least 9 units of iron, and at least 15 units of thiamine. How many ounces of each of the foods should be used to minimize the cost of the meal? a. Formulate the nutritionist's problem as an LP model. Define your decision variables precisely. b. Solve the problem graphically. Shade the feasible area properly. Label the corner points and give their

A nutritionist is planning a menu that includes foods A and B as its main staples. Suppose that each ounce of food A contains 2 units of protein, 1 unit of iron, and 1 unit of thiamine; each ounce of food B contains 1 unit of protein, 1 unit of iron, and 3 units of thiamine. Suppose that each ounce of A costs P3, while each ounce of B costs P4. The nutritionist wants the meal to provide at least 12 units of protein, at least 9 units of iron, and at least 15 units of thiamine. How many ounces of each of the foods should be used to minimize the cost of the meal? a. Formulate the nutritionist's problem as an LP model. Define your decision variables precisely. b. Solve the problem graphically. Shade the feasible area properly. Label the corner points and give their

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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kindly answer items (a), (b), and (c)

A nutritionist is planning a menu that includes foods A and B as its main staples. Suppose that each ounce of food A contains 2 units of protein, 1 unit of iron, and 1 unit of thiamine; each ounce of food B contains 1 unit of protein, 1 unit of iron, and 3 units of thiamine. Suppose that each ounce of A costs P3, while each ounce of B costs P4. The nutritionist wants the meal to provide at least 12 units of protein, at least 9 units of iron, and at least 15 units of thiamine. How many ounces of each of the foods should be used to minimize the cost of the meal? a. Formulate the nutritionist's problem as an LP model. Define your decision variables precisely. b. Solve the problem graphically. Shade the feasible area properly. Label the corner points and give their coordinates. Determine the slope of the objective function line. Sketch a typical objective function line and show HOW it intersects the candidate optimal point. Identify the optimal solution and give the corresponding value of the objective function. c. Verify your geometric solution by solving the LP using dual simplex method. Trace the “movement" of your dual simplex solutions from points outside the feasible area towards the optimal point. Based on the optimal dual simplex tableau, answer the following: d. If the needed nutrients were available in capsule form, how much (in units of pesos and/or centavos) would the nutritionist's client be willing to pay (i) For one capsule of iron? (ii) For one capsule of thiamine? e. What would be the maximum revenue for the person selling the capsule?
Transcribed Image Text:A nutritionist is planning a menu that includes foods A and B as its main staples. Suppose that each ounce of food A contains 2 units of protein, 1 unit of iron, and 1 unit of thiamine; each ounce of food B contains 1 unit of protein, 1 unit of iron, and 3 units of thiamine. Suppose that each ounce of A costs P3, while each ounce of B costs P4. The nutritionist wants the meal to provide at least 12 units of protein, at least 9 units of iron, and at least 15 units of thiamine. How many ounces of each of the foods should be used to minimize the cost of the meal? a. Formulate the nutritionist's problem as an LP model. Define your decision variables precisely. b. Solve the problem graphically. Shade the feasible area properly. Label the corner points and give their coordinates. Determine the slope of the objective function line. Sketch a typical objective function line and show HOW it intersects the candidate optimal point. Identify the optimal solution and give the corresponding value of the objective function. c. Verify your geometric solution by solving the LP using dual simplex method. Trace the “movement" of your dual simplex solutions from points outside the feasible area towards the optimal point. Based on the optimal dual simplex tableau, answer the following: d. If the needed nutrients were available in capsule form, how much (in units of pesos and/or centavos) would the nutritionist's client be willing to pay (i) For one capsule of iron? (ii) For one capsule of thiamine? e. What would be the maximum revenue for the person selling the capsule?
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