Linear Optimization Assignment:

in R Programming please

in R Programming please

in R Programming please

in R Programming please

1st Task

Linear programs are used to solve optimization problems where both the objective functions and constraints have linear relationships. Let's practice a linear programming case study through an example:

You are the founder of The Sodaz Company and you sell soda of two base products (Strawberry Soda, and Orange Soda.) You can sell them for a $12/pack and $24/pack profit respectively. Both sodas require water, CO2, and Flavoring as their main ingredients and you currently have the following quantities available 150 ounces of water, 480 grams of CO2, and 1190 pounds of flavoring.

• A batch of Strawberry Soda consumes 5 ounces of water, 4 grams of CO2, and 35 pounds of flavoring.
• A batch of the Orange Soda consumes 15 ounces of water, 4 grams of CO2, and 20 pounds of flavoring.

How many batches of Strawberry Soda and Orange Soda should you make to get the maximum profit possible?

2nd Task

The Sodaz Company is coming up with a hot new beverage called Grapye`. Because it is a special craft soda, it has a margin of $30/pack, It uses 10 ounces of water, 4g of CO2, and 15 pounds of flavoring.

The addition of this new soda requires that the company has to allocate its personnel to different manufacturing processes. Each of the batches takes 5 (Strawberry Soda), 10 (Orange Soda), and 20 (Grape Soda) hours of labor to make and we have only 5 employees full-time. If this is the production planning for a month of soda production, what is the optimal amount of each soda that must be produced to maximize profit?