a candy company has 130 pounds of cashews and 170 pounds of peanuts which they combine into different mixes good luck stats has half cash and half peanuts and sells for $7 a pound become a mix has one third cashews and two thirds peanuts and sells for 5.40 a pound how many pounds of each makes we prepared for maximum revenue

Question

a candy company has 130 pounds of cashews and 170 pounds of peanuts which they combine into different mixes good luck stats has half cash and half peanuts and sells for $7 a pound become a mix has one third cashews and two thirds peanuts and sells for 5.40 a pound how many pounds of each makes we prepared for maximum revenue

Answer 1

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Answer 2

To find the optimal number of pounds for each mix that will result in maximum revenue, we need to set up a system of equations.

Let's define the following variables:
- Let x be the number of pounds of the Good Luck Stats mix.
- Let y be the number of pounds of the Become a Mix.

We know the following information:
- The Good Luck Stats mix contains an equal amount of cashews and peanuts.
- The Becomes a Mix contains one-third cashews and two-thirds peanuts.
- The Good Luck Stats mix sells for $7 per pound.
- The Become a Mix sells for $5.40 per pound.
- The total weight of cashews available is 130 pounds.
- The total weight of peanuts available is 170 pounds.

Now, let's set up the equations:

1) The cashew equation:
Since the Good Luck Stats mix contains an equal amount of cashews and peanuts, we can represent this equation as:
0.5x = y/3

2) The peanut equation:
Since the Become a Mix contains one-third cashews and two-thirds peanuts, we can represent this equation as:
0.5x + (2/3)y = 170

3) The revenue equation:
The revenue from the Good Luck Stats mix is calculated as 7x, and the revenue from the Become a Mix is calculated as 5.40y. The total revenue is the sum of these two:
7x + 5.40y = Total Revenue

Now, let's solve this system of equations to find the values of x and y.

- Multiply the first equation by 2 to eliminate decimals:
x = (2/3)y

- Substitute x from the first equation into the second equation:
(2/3)y + (2/3)y = 170
(4/3)y = 170
y = (170 * 3) / 4
y = 127.5

- Substitute the value of y back into the first equation to find x:
x = (2/3) * 127.5
x = 85

Therefore, to maximize revenue, 85 pounds of the Good Luck Stats mix and 127.5 pounds of the Become a Mix should be prepared.