Math inequality question.. :/?
To fill an order for Sizzlin’ 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 below.
Red Hot Sauce yield:1pint
1 pint tomato sauce w/ onions
5 green peppers, diced
4 hot chili peppers
Scorchin’ Hot Sauce yield:1pint
1 pint tomato sauce w/ onions
4 green peppers, diced
8 hot chili peppers
Then select one solutions of the system and determine how many peppers you will have left over for each solution.
Do you have any idea how I’m supposed to do this question? I like figuring out math problems but when it comes to these sort of things I just get stuck.. :(
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5 Answers
It sounds like you consider both scenarios separately rather than solving for the max number of pints of sauce you can make… So I would do
Red -
5x <= 1050, 4y <= 1200 where x and y are the # of peppers you use
Scorchin -
4x <= 1050, 8y <= 1200
But maybe @CWOTUS knows better than I do. Apparently Ive kind of forgotten how to do these…
It will help to start making a picture of this – the graph, in other words.
Start by picking the axes of the graph. What is it that you’re going to be graphing? Green peppers vs. hot chili peppers? Pints of sauce vs. peppers? Once you’ve figured that out, then you can start to put some points on the graph, so you know at least a couple of points on the chart and can see the picture develop (and check your equation later).
What does your chart look like if you devote all of your ingredients to production of one kind of sauce or the other? (Thinking about this might help you to realize what your x and y axes are going to be representing.) Also, when you devote all of your production to one sauce or the other, what are you left with?
To help the graph take shape, you can also figure a half-and-half production position: What does the graph look like if you split your ingredients down the middle and make as much of either sauce as you can? And what is left over from that production? What additional production of the two sauces can you make from the leftovers of each mode of production?
Let x be the amount of the first sauce and y be the amount of the second sauce. The number of green peppers used is 5x + 4y and the inequality that this must satisfy is 5x + 4y <= 1050, Write a similar inequality for the hot peppers. Express both equations in the form y <= mx + b. The possible solutions are the parts of the coordinate plane that is below both lines.
This is an example of a problem in Linear Programming. Read online tutorials & worked examples.
@gasman, I think it is leading up to linear programming, but there is no objective function to maximize or minimize.
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