**Hot! Hot! Hot!**

**By: Kendall Nelson. Mr. Kirkland's Math III first period**

*I am the owner of a sizzlin' hot sauce company. We make two different types of sauces; Red Hot Sauce, and Scorchin' Hot Sauce. As the owner of this company my plan is to minimize costs, maximize profit, and keep my customers satisfied by filling orders promptly. The recipes for my famous sauces are:*

## Activity One

To fill an order for Sizzlin' Sauce sauces, I purchased 1050 green peppers and 1200 hot chili peppers. To represent how many peppers are used in each recipe I created the inequalities: 5r+4s<=1050 and 4r+8s<=1200. These inequalities then reduced to: s<=-5/4+262.5 and s<=-1/2r+150. With these inequalities I was able to graph two lines and create a feasible region for the various amount of pints that can be made. I used the point (70,100) and plugged it in to the inequalities to conclude that if 70 pints of Red Hot Sauce, and 100 pints of Scorchin' Hot Sauce is made, then 300 green peppers and 120 hot chili peppers will be left over.

## Activity Two :

After filling the Sizzlin' Sauce order, my next goal is to maximize profit. Suppose $1.20 profit is made on Red Hot Sauce, and $1.00 profit is made on Scorchin' Hot Sauce. To get a maximum profit of $255, one hundred fifty pints of Red Hot Sauce should be made and sold, and seventy-five pints of Scorchin' Hot Sauce should be made and sold. The calculations are shown below.

# Activity Three

**If we refer back to the Recipes**

**If we refer back to the Recipes**

## To maintain a profit of $1.20 for Red Hot Sauce and $1.00 profit for Scorchin' Hot Sauce, then Red Hot Sauce will be sold for $8.25 and Scorchin' Hot Sauce will be sold for $9.48.

# Activity Four

I can now sell my sauces to a supermarket chain, a local grocery store, and a speciality store. The super market chain will buy 288 pints every 8 weeks, the grocery store will buy 60 pints every 4 weeks, and the speciality store will buy 24 pints each week.

To fill all these orders, 75 pints of sauce should be produced each week. The spreadsheet below shows the production of 75 pints each week, the subtraction of the speciality store buying 24 pints each week, the grocery store buying 60 pints every 4 weeks, and the super market chain buying 288 pints every 8 weeks. This process will just continue to repeat in the next and upcoming weeks.