A company manufactures two products X and Y by means of two processes A and B. The maximum capacity of process A is 1750 hours and of process B 4000 hours. Each unit of product X requires 3 hours in A and 2 hours in B, while each unit of product Y requires 1 hour in A and 4 in B. Use the algebraic method to calculate how many units of products X and Y are produced if the maximum capacity available is utilized?
A=3X=1750
B=2X=4000
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A=Y=1750
B=4Y=4000
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3X+Y=1750
2X+4Y=4000
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-Solve for x,y when x=0 and y=0
-Plug in and solve equations
x= 583.33
y=1000
To solve this problem using the algebraic method, we need to set up a system of equations based on the given information. Let's use the variables X and Y to represent the number of units of products X and Y, respectively.
We know that each unit of product X requires 3 hours in process A and 2 hours in process B, while each unit of product Y requires 1 hour in process A and 4 hours in process B. Therefore, we can write the following equations:
3X + Y = 1750 (equation 1)
2X + 4Y = 4000 (equation 2)
Equation 1 represents the capacity constraint for process A, where 3X represents the total hours required for producing X units of product X, and Y represents the total hours required for producing Y units of product Y. The sum of these hours should not exceed the maximum capacity of process A, which is 1750 hours.
Similarly, equation 2 represents the capacity constraint for process B, where 2X represents the total hours required in process B for producing X units of product X, and 4Y represents the total hours required in process B for producing Y units of product Y. The sum of these hours should not exceed the maximum capacity of process B, which is 4000 hours.
Now, we can solve this system of equations to find the values of X and Y.
First, let's solve equation 1 for Y:
Y = 1750 - 3X
Now, substitute this value of Y in equation 2:
2X + 4(1750 - 3X) = 4000
2X + 7000 - 12X = 4000
-10X = -3000
X = 300
Now substitute the value of X back into equation 1 to find Y:
3(300) + Y = 1750
900 + Y = 1750
Y = 850
Therefore, X = 300 and Y = 850. This means that 300 units of product X and 850 units of product Y can be produced if the maximum capacity available is utilized.