# Chapter 2 Project

### A. Moore Kirkland 1st period Math III

Suppose you are the owner of the Sizzlinâ€™ Sauce Company. Your company makes two different kinds of sauce, Red Hot Sauce and Scorchinâ€™ Hot Sauce (the recipes for the sauces are listed below).  As the owner of a successful business, you want to minimize costs, maximize profit, and keep customers satisfied by filling orders promptly.

To fill an order for Sizzlin' Sauce sauces, you bought 1050 green peppers and 1200 hot chili peppers.  Write and graph a system of inequalities to represent the number of pints of each kind of sauce you can make.  Refer to the recipes above.  Then, select one solution   from the feasible region (shaded area) and determine how many peppers you will have left over after you have made the desired number of pints for each type of sauce.

Suppose you make \$1.20 profit on one pint of Red Hot Sauce and \$1.00 profit on one pint of Scorchin' Hot Sauce.  Using the restrictions  from the system of inequalities, decide how many pints of each type of sauce you should make to maximize your profit.

The cost of one green pepper is \$1.00 and the cost of one hot chili pepper is \$0.50. Find the cost of producing one pint of each type of sauce and decide what selling price should be set for the sauces in order for you to maintain your profit.

You can sell your sauce to a supermarket chain, a local grocery, and a specialty store.  The supermarket chain will buy 288 pints every eight weeks, the grocery 60 pints every four weeks, and the speciality store 24 pints every week.  How many pints of sauce should you make each week to fill these orders if you make the same amount every week and the type of sauce does not matter?

To fill these orders every time without having any extra pints in the end, you would need to make 75 pints every week.  The "Number bought" column represents the number of pints purchased every week by any or all of the stores.  After eight weeks, the number bought adds up to 600, which corresponds with the total number made in the same amount of time.  The last column tells how many pints are left over after all of the purchases have been made for that week.

Conclusion:

To maximize your profit, you would make 150 pints of Red Hot Sauce and 75 pints of Scorchin' Hot Sauce for a profit of \$255.00.  To maintain this profit, you would sell the Red Hot Sauce for \$7.66 with a \$0.54 tax for a final price of \$8.20, and you would sell the Scorchin' Hot Sauce for \$8.41 with a \$0.59 tax for a final price of \$9.00.  Every week you would need to make 75 pints to fill the orders and not have any remaining so your business would be more efficient.

Literacy Skills:

To be able to separate my thoughts and go step by step, I numbered the sentences and placed them in a brace map in order to have a more organized problem.