Inequalities word problem, Algebra

Activity 1: Graphing
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 how many pints of each kind of sauce you can make. Use the recipes below.
• Select one solution of the system and determine how many peppers you will have left over.

Sizzlin'' Sauces Recipes
Scorchin'' Hot Sauce Ingredients Red Hot Sauce Ingredients
Yield: 1 pint
1 pint tomato sauce with onions
4 green peppers, diced
8 hot chili peppers, seeded and diced Yield: 1 pint
1 pint tomato sauce with onions
5 green peppers, diced
4 hot chili peppers, seeded and diced
Activity 2: Analyzing
Suppose you make $1.20/pt profit on Red Hot Sauce and $1.00/pt profit on Scorchin'' Hot Sauce. Using the restrictions from Activity 1, decide how much of each sauce you should make and sell to maximize your profit. What is the maximum profit?
Activity 3: Researching
Visit a local grocery store to estimate the cost of each sauce ingredient. Remember that buying in large quantities can save you money.
• Find the cost to produce 1 pt of each type of sauce.
• What selling price will you set for each sauce to maintain your profit?
Activity 4: Organizing
You can sell your sauce to a supermarket chain, a local grocery store, and a specialty store. The supermarket chain will buy 288 pints at a time, every eight weeks. The grocery store will buy 60 pints every four weeks, and the specialty store will buy 24 pints each week.
• How much sauce should you produce each week to fill these orders? Presume that you want to produce the same number of pints each week, and that the type of sauce is not a factor in filling these orders.
• Design a spreadsheet to track your stock of sauce after each week. Use cell formulas.
Finishing the Chapter Project
The activities should help you to complete your project. Your report should include your analysis of the cost of producing Sizzlin'' Sauces. Include your profit analysis and production spreadsheet. Illustrate your reasoning and decisions with graphs.
Reflect and Revise
Present your analysis to a family member or friend. Decide if your work is complete, clear, and convincing. If needed, make changes to improve your presentation.
Extending the Project
Are there other expenses you could expect in addition to those you have already considered? Estimate them. Modify your recommendations if necessary.
Chapter Project Checklist
Have you done all of the following?
• Made sure that answers are reasonable
• Checked your work with a graphing calculator
• Documented your information
• Remembered that you will produce the same amount of sauce every week
• Besides the cost of ingredients, what information would need to be taken into consideration to accurately determine the profit? How would you go about finding this information?

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Inequalities word problem, Algebra

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