Suppose in an LP, we have the following constraints: What is the x value at the intersection point between the two constraint boundary lines x+6 y=8 and 7x + 5y

Question

Suppose in an LP, we have the following constraints:

What is the x value at the intersection point between the two constraint boundary lines x+6 y>=8 and 7x + 5y <= 35 ? (Round your answer to 4 decimals. )

BlackTom AI · Accepted Answer

To find the intersection point of the two constraint boundary lines, we set up the equations from their boundaries: x + 6y = 8 and 7x + 5y = 35.

First, express x from the first equation: x = 8 − 6y.

Substitute this into the second equation:
7(8 − 6y) + 5y = 35
=> 56 − 42y + 5y = 35
=> 56 − 37y = 35.

Solve for y: −37y = 35 − 56 = −21, so y = (−21)/(−37) = 21/37 ≈ 0.567567.

Now plug y back into x = 8 − 6y:
x = 8 − 6*(21/37) = 8 − 126/37 = (296/37) − (126/37) = 170/37 ≈ 4.5950.

Therefore, the intersection point is at x ≈ 4.5950 (to four decimals) and y ≈ 0.5676. The requested x-value at the intersection is 4.5950.

BU.520.601.T2.FA25 Final Exam

Suppose in an LP, we have the following constraints: What is the x value at the intersection point between the two constraint boundary lines x+6 y>=8 and 7x + 5y <= 35 ? (Round your answer to 4 decimals. )

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