Algebra 2

sauce 1: 5 green peppers + 4 hot peppers
sauce 2: 4 green peppers + 8 hot peppers
I have 1050 green peppers and 1200 hot peppers
Profit sauce 1 :$1.20
Profit sauce 2: $ 1.00

I made a system of inequalities:
5x +4y > 1
4x +8y > 1
x< 1050
y< 1200

I calculated I can make :
210 pints of sauce 1 with left over 360 hot peppers or
150 pints of sauce 2 with left over 450 green peppers

How much of each sauce should I make to max profit and what is the max profit?

If I make only sauce 1 my profit will be $ 252
if I only make sauce 2 my profit will be only $150

But I am confused about how calculate to graph this information so it shows my total profit

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  1. looks like you haven't thought out just what your variables represent.

    In the first two equations, it appears that x is the number of batches of sauce 1, y is the number of batches of sauce 2, so 5x+4y is the number of green peppers required, and 4x+8y is the number of red peppers required.

    In the 2nd set of conditions, x and y appear to be the number of peppers.

    So, what you need is (with x,y the number of pints of sauce):

    x >= 1
    y >= 1
    5x+4y <= 1050
    4x+8y <= 1200

    Now, to maximize profit, you want to maximize

    p = 1.20x + 1.00y

    subject to the above conditions. Using your favorite linear optimization calculator, you will find that

    max p = $255.00 at
    x=150
    y=75

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  2. thank you :) You explained it so easy!

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