A candy manufacturer makes two types of special candy, say A and B. Candy A consists of equal parts of dark chocolate and caramel and Candy B consists of two parts of dark chocolate and one part of walnut. The company has in stock 430 kilograms of caramel, 360 kilograms of dark chocolate, and 210 kilograms of walnuts. The company sells Candy A for P285 and Candy B for P260 per kilograms. How much of each candy should the manufacturer produce to maximize profit?
P=285x+260y
x+2y<360 - eq. 1
X<430 -eq.2
Y<210 -eq.3
--GRAPHING THE INEQUALITIES--
Eq.1
X=0,y=180
Y=0,x=360
Eq.2 and Eq. 3, no need it is given
--Extreme Points--
(0,180)
(360,0)
(-60,150)
(430,-35)
Substitute these points to our Objective Function P
(0,180) = 46,800
(360,0)=102,600
(-60,150)=21,900
(430,-35)=113,450
So, the answer is (x=430, y=-35)
*please double check if there are errors
Eh Alright lets see what is going on here
So do you think you would add subtract multiply or divide when you pick one of those add, subtract, multiply, or divide it and then you will have your answer
Where did you get the (-60,150) and (430,-35)? Thanks!
To maximize profit, we need to determine how many kilograms of each candy the manufacturer should produce.
Let's assume the manufacturer produces x kilograms of Candy A and y kilograms of Candy B.
We'll start by setting up the constraints based on the available ingredients:
For caramel: The amount used for Candy A is x kilograms, so we have the constraint x <= 430.
For dark chocolate: The amount used for Candy A is also x kilograms, and the amount used for Candy B is 2y kilograms, so we have the constraint x + 2y <= 360.
For walnuts: The amount used for Candy B is y kilograms, so we have the constraint y <= 210.
Next, let's define the objective function, which is the profit made from selling the candies:
Profit = (285 * x) + (260 * y)
Now, we can solve this linear programming problem with the given constraints and objective function.
One way to solve this is by using graphical methods, but it can be time-consuming and less accurate for larger problems. Instead, we can use linear programming software or online tools to find the optimal solution.
After solving the linear programming problem, we can determine the values of x and y that will maximize the profit. These values represent how much of each candy the manufacturer should produce.