1. The Sonoma Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $0.85 to produce a jar of applesauce and $0.75 to produce a bottle of apple juice. The company has a policy that at least 25 percent but no more than 65 percent of its output must be applesauce. The company wants to meet but not exceed the demand for each product. The marketing manager estimates that the demand for applesauce is a maximum of 4500 jars, plus an additional 4 jars for each $1 spent on advertising for applesauce. The maximum demand for apple juice is estimated to be 3800 bottles, plus an additional 5 bottles for every $1 spent on advertising for apple juice. The company has $16,500 to spend on producing and advertising its two products. Applesauce sells for $2 per jar, and apple juice sells for $1.50 per bottle. Formulate a linear optimization model to help the company determine how many units of each product to produce, and how much advertising to spend on each product, in order to maximize profit. (You do not need to find the optimal solution to the model you formulate

2. Best West Airlines is a new airline that seeks to please its customers by providing pretzels, cashews, juice, and milk on flights. They would like to decide how many cartons of each to carry on their next flight in order to maximize the enjoyment of their passengers. However, there are also some constraints that restrict what they can carry. The following table shows some information about the different products (all figures are per carton): Pretzels Cashews Juice Milk Weight (ounces) 30 40 60 50 Volume (cubic inches) 12 10 14 15 Enjoyment Value 16 35 45 35 a) Define decision variables that can be used in a linear optimization formulation of Best West Airlines’ problem. b) Write an objective function for BestWest Airlines. Write constraints that reflect the following: c) There is a limit of 650 ounces on the weight of food and drinks that the plane can carry. d) The combined number of cartons of juice and milk must be no more than the combined number of cartons of pretzels and cashews. e) Pretzels should account for no more than 30% of the total volume of food and drinks.

3. Graph the feasible region for the following linear optimization model:

(a) Graph the constraints and identify the feasible region.

(b) Choose a value and draw a line representing all combinations of x and y that make the objective function equal to that value.

(c) Determine the optimal values of x and y.

(d) Label the optimal solution(s) on your graph.

(e) Calculate the optimal value of the objective function.

(a) Graph the constraints and identify the feasible region.

(b) Choose a value and draw a line representing all combinations of x and y that make the objective function equal to that value.

(c) Determine the optimal values of x and y.

(d) Label the optimal solution(s) on your graph.

(e) Calculate the optimal value of the objective function.

(a) Graph the constraints and identify the feasible region.

(b) Choose a value and draw a line representing all combinations of x and y that make the objective function equal to that value.

(c) Determine the optimal values of x and y.

(d) Label the optimal solution(s) on your graph.

(e) Calculate the optimal value of the objective function.

Maximize Subject to 3x + 4y -x + 2y 8 x + 2y 12 2x + y 16 x, y 0 4. Consider the linear optimization model Minimize 4x + 2y Subject to 5x + 15y 20x + 5y 40 15x + 2y 60 x, y 0 50 5. Consider the linear optimization model Minimize 2x + 4y Subject to 4x + 2y 28 3x + 4y > 12 2x + 3y 12 x, y 0 6. Consider the linear optimization model Maximize 4x + 2y Subject to 2x + y 16 -x + y 7 x 6 x, y 0