Question

A generous candy company decides to give 3 different treats as freebies to visitors at their awesome factory: Grapefruit bars, candied carrots, and apple caramels. Each requires different amounts of cooking time and sugar, both of which are limited. Each treat also offers a different reward value (satisfaction) to the visitor that gets it. The amount of resources and their availability, as well as the reward for each treat, is listed below. Cooking time (mins) Sugar needed (oz) satisfaction Grapefruit bars 27 12 3 Candied carrots 38 27 5 Apple caramels 45 18 4.2 Available 4700 2300 a) Formulate an integer program that maximizes the total satisfaction felt by the visitors that get the treats made by the candy company. Define all variables, objective function, constraints, and restrictions on variables. b) To accommodate health-minded people, the workers have suggested using Stevia sweetener. The candy company has a total 2900 ounces of Stevia. In replacement of sugar, Grapefruit bars need 30 ounces of Stevia, Candied carrots need 17 ounces of Stevia, and Apple caramels need 25 ounces of Stevia. The workers will only use either sugar or Stevia, not both, but isn’t sure which one will produce the most happiness. Change/amend your formulation in (a) as necessary to incorporate this decision. c) Suppose the manager asks workers to focus on making only two types of treats. Change/amend your formulation in (a) as necessary to incorporate this restriction. (you can ignore (b) for this question). Explain your reasoning.

A generous candy company decides to give 3 different treats as freebies to visitors at their awesome factory: Grapefruit bars, candied carrots, and apple caramels. Each requires different amounts of cooking time and sugar, both of which are limited. Each treat also offers a different reward value (satisfaction) to the visitor that gets it. The amount of resources and their availability, as well as the reward for each treat, is listed below.

Cooking time (mins) Sugar needed (oz) satisfaction
Grapefruit bars 27 12 3
Candied carrots 38 27 5
Apple caramels 45 18 4.2
Available 4700 2300

a) Formulate an integer program that maximizes the total satisfaction felt by the visitors that get the treats made by the candy company. Define all variables, objective function, constraints, and restrictions on variables.

b) To accommodate health-minded people, the workers have suggested using Stevia sweetener. The candy company has a total 2900 ounces of Stevia. In replacement of sugar, Grapefruit bars need 30 ounces of Stevia, Candied carrots need 17 ounces of Stevia, and Apple caramels need 25 ounces of Stevia. The workers will only use either sugar or Stevia, not both, but isn’t sure which one will produce the most happiness. Change/amend your formulation in (a) as necessary to incorporate this decision.

c) Suppose the manager asks workers to focus on making only two types of treats. Change/amend your formulation in (a) as necessary to incorporate this restriction. (you can ignore (b) for this question). Explain your reasoning.

A generous candy company decides to give 3 different treats as freebies to visitors at their awesome factory: Grapefruit bars, candied carrots, and apple caramels. Each requires different amounts of cooking time and sugar, both of which are limited. Each treat also offers a different reward value (satisfaction) to the visitor that gets it. The amount of resources and their availability, as well as the reward for each treat, is listed below.

Cooking time (mins) Sugar needed (oz) satisfaction
Grapefruit bars 27 12 3
Candied carrots 38 27 5
Apple caramels 45 18 4.2
Available 4700 2300

a) Formulate an integer program that maximizes the total satisfaction felt by the visitors that get the treats made by the candy company. Define all variables, objective function, constraints, and restrictions on variables.

b) To accommodate health-minded people, the workers have suggested using Stevia sweetener. The candy company has a total 2900 ounces of Stevia. In replacement of sugar, Grapefruit bars need 30 ounces of Stevia, Candied carrots need 17 ounces of Stevia, and Apple caramels need 25 ounces of Stevia. The workers will only use either sugar or Stevia, not both, but isn’t sure which one will produce the most happiness. Change/amend your formulation in (a) as necessary to incorporate this decision.

c) Suppose the manager asks workers to focus on making only two types of treats. Change/amend your formulation in (a) as necessary to incorporate this restriction. (you can ignore (b) for this question). Explain your reasoning.

Added by Eugenia S.

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