17 of 18 Set up and solve projects 1-4 from Section 7.2 using the simplex method, and set up and solve the exercises 1-7 from Section 7.1 using the simplex method. 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! and additive 2. The following conditions must hold for their use Barmfal 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 cach car's gasoline 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: $1.53/1b for additive 1 and 54/1b 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. List the decision variables and define them. I. List the objective function. c List the resources that constrain this problem. d. Graph the feasible repon. e Label all intersection points of the feasible region. . Plot the objective function in a different color (highlight the objective function line, ir necessary) and label it the ISO-profit line. Clearly indicate the point that is the optimal solution on the graph. List the coordinates of the optimal solution and the value of the objective function. 1. 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 and at least 0.3 lb of additive 2. Use graphical LP methods to help determine whether you should buy this TV offer. Support your recommendation Write a one-page cover letter to the boss of your company that summarizes the results that you found 17 of 18 Set up and solve projects 1-4 from Section 7.2 using the simplex method, and set up and solve the exercises 1-7 from Section 7.1 using the simplex method. 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! and additive 2. The following conditions must hold for their use Barmfal 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 cach car's gasoline 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: $1.53/1b for additive 1 and 54/1b 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. List the decision variables and define them. I. List the objective function. c List the resources that constrain this problem. d. Graph the feasible repon. e Label all intersection points of the feasible region. . Plot the objective function in a different color (highlight the objective function line, ir necessary) and label it the ISO-profit line. Clearly indicate the point that is the optimal solution on the graph. List the coordinates of the optimal solution and the value of the objective function. 1. 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 and at least 0.3 lb of additive 2. Use graphical LP methods to help determine whether you should buy this TV offer. Support your recommendation Write a one-page cover letter to the boss of your company that summarizes the results that you found