Input/output Product Mix problem

Scenario:

Alyson has just been hired by Tyson as a manager to oversee the poultry component of the company. Fourth day of your job, her vice president calls you in and presents you with a problem.

The problem is as follows:

Among many products produced by Tyson, chicken nuggets and popcorn chicken, are two very popular products. To make one 20 oz chicken nugget pack it takes 4 whole chickens. One cannot use all chicken parts to make chicken nuggets the remaining parts are used to make other products such as chicken wings of different styles. Similarly, to make one 20 oz chicken popcorn, it takes 3 chickens and 2 units of special sauce X.

As a manager you know the profit per 20 oz bag of chicken nugget is $.95 and profit per 20 oz bag of chicken popcorn is $1.10.

Your product processing plant gets 900 chickens and 408 X sauces every morning. Your VP wants to make at least twice the number of chicken popcorn as chicken nugget as the profit from chicken popcorn is higher than chicken nugget. Also, your VP wants to make at least 50 popcorn chicken per day as sauce X gets spoiled in few days.

After, giving this information your VP asks you:

Problem:

How many chicken nuggets and popcorn chicken should we produce to make the maximize profits?

Output Product mix problem

Scenario:

Alex has recently started a local agribusiness, Mr. Hauns business, two months ago and makes products N and E each week to sell to another local business, Taylors Business.

Note: E and N could be anything including your different variety of seeds. And, Taylor can be local seed dealer and/or farmer.

Taylor tells Alex that her business will buy between 10 and 40 N each week. Based on last months sales, Alex has figured out that that each week Taylor has bought at least twice the number of E as N. Also, since Alex just in the early stages he only has two employees, himself and his significant other, so he cannot make more than 50 pieces of N and E combined per week.

As a business owner Alex knows N makes a profit of $25 per piece and E makes a profit of $10 per piece. Almost being a college graduate Alex knows that he wants written contract for legal purpose and to keep things clear.

So, Alex is planning on making a sales contract with Taylors business for the next month. Given above information on profit and constraints:

Problem:

How many N and how many E should Alex sell Taylor to maximize his profits?

Once you figure out the optimal N and E you will sign a contract to deliver (and Barry to buy) those many Ns and Es.

We are using Lindo to do the calculations. For that you need to fill in the following for each problem:

Max (Linear objective function)

Linear constraints including non-negative constraints