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
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
thank you :) You explained it so easy!
To graph the information and determine the total profit, we can use linear programming.
Let's define our variables:
Let x represent the number of pints of sauce 1 produced.
Let y represent the number of pints of sauce 2 produced.
Next, let's define our objective function and constraints:
Objective function:
We want to maximize the profit, so our objective function is:
Profit = 1.20x + 1.00y
Constraints:
1) We have limited resources - the number of green peppers available and the number of hot peppers available. From the given information, we have:
5x + 4y ≤ 1050 (green pepper constraint)
4x + 8y ≤ 1200 (hot pepper constraint)
2) We cannot produce a negative number of pints, so we have the additional constraints:
x ≥ 0
y ≥ 0
Now, we can graph these constraints to find the feasible region:
1) Start by graphing the equalities:
5x + 4y = 1050 (green pepper constraint)
4x + 8y = 1200 (hot pepper constraint)
2) Shade the region BELOW each line, to represent the inequalities (≤). This region represents the feasible region.
3) Shade the region in the feasible region that satisfies the non-negativity constraints, x ≥ 0 and y ≥ 0.
4) Now, look for the intersection point of the feasible region and calculate the profit at that point using the objective function. The point with the maximum profit will be the optimal solution.
5) Finally, you can calculate the maximum profit by substituting the values of x and y into the objective function.
From the information you provided, it seems that making 210 pints of sauce 1 and 150 pints of sauce 2 will give you the maximum profit. To calculate the maximum profit, substitute these values into the objective function:
Profit = 1.20(210) + 1.00(150) = $432
Therefore, if you make 210 pints of sauce 1 and 150 pints of sauce 2, your maximum profit will be $432.