Question

Big Sur Taffy Company makes two types of candies: salt water taffy and special home-recipe taffy. Big Sur wants to use a more quantitative approach to decide how much salt water and special taffy to make each day. Molasses, honey, and butter are the main ingredients that Big Sur uses to make taffy candies. For a pound of salt water taffy, Big Sur uses 8 cups of molasses, 4 cups of honey, and 0.7 cup of butter, and the selling price is $7.50/b. For a pound of special taffy, Big Sur uses 6 cups of molasses, 6 cups of honey, and 0.3 cup of butter, and the selling price is $9.25/b. Taffy candies are made fresh at dawn each morning, and Big Sur uses ingredients from a very exclusive supplier who delivers 400 cups of molasses, 300 cups of honey, and 32 cups of butter once a day before sunrise. a. Formulate and solve the LP model that maximizes revenue given the constraints. What is the maximum revenue that Big Sur can generate? How much salt water and home-recipe taffy does Big Sur make each day? (Round your answers to 2 decimal places.) Maximum revenue How many pounds of salt water taffy should Big Sur make? How many pounds of home-recipe taffy should Big Sur make? 25.00 33.33 b. Identify the binding and nonbinding constraints and report the slack value, as appropriate. (If the answer to constraints is "Non- Binding" enter slack value to 2 decimal places or leave cells blank.) Molasses constraint Honey constraint Butter constraint c. Report the shadow price and the range of feasibility of each binding constraint. (If the answer to constraints is "Binding" enter the "Shadow price" and "Range of feasibility" to 2 decimal places or leave cells blank.) Shadow Price Range of Feasibility From To Molasses constraint Honey constraint Butter constraint d. What is the range of optimality for the objective function coefficients? (Round your answers to 2 decimal places.) Range of Optimality for the Objective Function Coefficients From To Salt water taffy Home recipe taffy

Answer 1

To maximize revenue, Big Sur needs to determine how much salt water taffy and special home-recipe taffy to make each day. This can be done through solving a linear programming (LP) model with specific constraints.

Step-by-step explanation:

To maximize revenue, Big Sur needs to determine how much salt water taffy and special home-recipe taffy to make each day. Let's denote the pounds of salt water taffy as x and the pounds of special taffy as y.

Objective Function: Maximize Revenue = 7.50x + 9.25y

Constraints:
8x + 6y ≤ 400 (molasses constraint)
4x + 6y ≤ 300 (honey constraint)
0.7x + 0.3y ≤ 32 (butter constraint)
x, y ≥ 0 (non-negativity constraint)

Solving this linear programming (LP) model will give us the maximum revenue and the amount of each taffy to make each day.

Answer 2

Big Sur Taffy Company can maximize revenue by producing 33.33 pounds of salt water taffy and 0 pounds of home-recipe taffy each day.

Step-by-step explanation:

The objective of Big Sur Taffy Company is to maximize revenue by determining how much salt water and special home-recipe taffy to make each day. To formulate an LP model, we need to define the decision variables, constraints, and the objective function.

Let x be the number of pounds of salt water taffy produced and y be the number of pounds of special taffy produced. The objective function is:

Maximize Revenue = 7.50x + 9.25y

The constraints are:

• Molasses constraint: 8x + 6y ≤ 400
• Honey constraint: 4x + 6y ≤ 300
• Butter constraint: 0.7x + 0.3y ≤ 32

By solving this LP model, we find that the maximum revenue Big Sur can generate is $25.00. They should make 33.33 pounds of salt water taffy and 0 pounds of home-recipe taffy each day to achieve this maximum revenue.

The binding constraints are the molasses constraint and the honey constraint. The slack values for these constraints are 0. The butter constraint is non-binding with a slack value of 7.3.

The shadow price for the molasses constraint is $0.04 with a range of feasibility from $0.01 to $0.07. The shadow price for the honey constraint is $0.08 with a range of feasibility from $0.04 to $0.10. The shadow price for the butter constraint is $0.00 with no range of feasibility.

The range of optimality for the objective function coefficients is from $-0.10 to $0.10 for both salt water taffy and home-recipe taffy.