1) a-d
1. With the rising cost of gasoline and increasing prices to consumers, the use of additives to enhance gasoline performance is being considered. Consider two additives: additive 1 and additive 2. The following conditions must hold for their use: Harmful carburetor deposits must not exceed 1/2 lb for each car's gasoline tank. The quantity of additive 2 plus twice the quantity of additive I must be at least 1/2 lb for each car's gasolinc tank. One pound of additive I will add 10 octane units per tank, and 1 lb of additive 2 will add 20 octane units per tank. The total number of octane units added must not be less than six (6) Additives are expensive: 51.53/1b for additive 1 and 54/lb for additive 2. We want to determine the quantity of each additive that will meet the above restrictions and will minimize their cost while meeting the following requirements. a. List the decision variables and define them. b. List the objective function. c. List the resources that constrain this problem. d. Graph the feasible region. e. Label all intersection points of the feasible region. f. Plot the objective function in a different color (highlight the objective function line, if necessary) and label it the ISO-profit line. g. Clearly indicate the point that is the optimal solution on the graph. h. List the coordinates of the optimal solution and the value of the objective function. i. Assume now that a manufacturer of additives has the opportunity to sell you a nice special TV deal to deliver at least 0.5 lb of additive I and at least 0.3 ib of additive 2. Use graphical LP methods to help determine whether you should buy this TV offer. Support your recommendation 1. Write a one-page cover letter to the boss of your company that summarizes the results that you found. 2. A farmer has 30 acres on which to grow tomatoes and corn. Each 100 bushels of toma- toes require 1,000 gallons of water and 5 acres of land. Each 100 bushels of corn require 6,000 gallons of water and 2% acres of land. Labor costs are si per bushel for both com and tomatoes. The farmer has available 30,000 gallons of water and S750 in capital. He knows that he cannot sell more than 500 bushels of tomatoes or 475 bushels of corn. He estimates a profit of $2 on each bushel of tomatoes and $3 for each bushel of corn. How many bushels of each should he raise to maximize profits? Meet the following requirements: a. List the decision variables and define them. b. List the objective function. c. List the resources that constrain this problem. d. Graph the feasible region. e. Label all intersection points of the feasible region. Plot the objective function in a different color (highlight the objective function line, if necessary) and label it the ISO-profit line. 8. Clearly indicate on the graph the point that is the optimal solution. h. List the coordinates of the optimal solution and the value of the objective function. i. Assume now that farmer has the opportunity to sign a nice contract with a grocery store to grow and deliver at least 300 bushels of tomatoes and at least 500 bushels of corn Use graphical LP methods to help recommend a decision to the farmer. Support your recommendation. j. If the farmer can obtain an additional 10,000 gallons of water for a total cost of $50, is it worth it to obtain the additional water? Determine the new optimal solution caused by adding this level of resource. k. Write a one-page cover letter to your boss that summarizes the result that you found. 1. With the rising cost of gasoline and increasing prices to consumers, the use of additives to enhance gasoline performance is being considered. Consider two additives: additive 1 and additive 2. The following conditions must hold for their use: Harmful carburetor deposits must not exceed 1/2 lb for each car's gasoline tank. The quantity of additive 2 plus twice the quantity of additive I must be at least 1/2 lb for each car's gasolinc tank. One pound of additive I will add 10 octane units per tank, and 1 lb of additive 2 will add 20 octane units per tank. The total number of octane units added must not be less than six (6) Additives are expensive: 51.53/1b for additive 1 and 54/lb for additive 2. We want to determine the quantity of each additive that will meet the above restrictions and will minimize their cost while meeting the following requirements. a. List the decision variables and define them. b. List the objective function. c. List the resources that constrain this problem. d. Graph the feasible region. e. Label all intersection points of the feasible region. f. Plot the objective function in a different color (highlight the objective function line, if necessary) and label it the ISO-profit line. g. Clearly indicate the point that is the optimal solution on the graph. h. List the coordinates of the optimal solution and the value of the objective function. i. Assume now that a manufacturer of additives has the opportunity to sell you a nice special TV deal to deliver at least 0.5 lb of additive I and at least 0.3 ib of additive 2. Use graphical LP methods to help determine whether you should buy this TV offer. Support your recommendation 1. Write a one-page cover letter to the boss of your company that summarizes the results that you found. 2. A farmer has 30 acres on which to grow tomatoes and corn. Each 100 bushels of toma- toes require 1,000 gallons of water and 5 acres of land. Each 100 bushels of corn require 6,000 gallons of water and 2% acres of land. Labor costs are si per bushel for both com and tomatoes. The farmer has available 30,000 gallons of water and S750 in capital. He knows that he cannot sell more than 500 bushels of tomatoes or 475 bushels of corn. He estimates a profit of $2 on each bushel of tomatoes and $3 for each bushel of corn. How many bushels of each should he raise to maximize profits? Meet the following requirements: a. List the decision variables and define them. b. List the objective function. c. List the resources that constrain this problem. d. Graph the feasible region. e. Label all intersection points of the feasible region. Plot the objective function in a different color (highlight the objective function line, if necessary) and label it the ISO-profit line. 8. Clearly indicate on the graph the point that is the optimal solution. h. List the coordinates of the optimal solution and the value of the objective function. i. Assume now that farmer has the opportunity to sign a nice contract with a grocery store to grow and deliver at least 300 bushels of tomatoes and at least 500 bushels of corn Use graphical LP methods to help recommend a decision to the farmer. Support your recommendation. j. If the farmer can obtain an additional 10,000 gallons of water for a total cost of $50, is it worth it to obtain the additional water? Determine the new optimal solution caused by adding this level of resource. k. Write a one-page cover letter to your boss that summarizes the result that you found
