Answer:
Equation: 7x - 23 = 25 + x
Solution: x = 8
Step-by-step explanation:
7x - 23 = 25 + x
1. Subtract 25 from both sides:
7x - 23 - 25 = 25 - 25 + x
7x - 48 = x
2. Subtract 7x from both sides to get x on one side:
7x - 7x - 48 = x - 7x
- 48 = -6x
3. Divide both sides by -6 to get x by itself:
8 = x
8 is the solution
Answer:
1. Objective function is a maximum at (16,0), Z = 4x+4y = 4(16) + 4(0) = 64
2. Objective function is at a maximum at (5,3), Z=3x+2y=3(5)+2(3)=21
Step-by-step explanation:
1. Maximize: P = 4x +4y
Subject to: 2x + y ≤ 20
x + 2y ≤ 16
x, y ≥ 0
Plot the constraints and the objective function Z, or P=4x+4y)
Push the objective function to the limit permitted by the feasible region to find the maximum.
Answer: Objective function is a maximum at (16,0),
Z = 4x+4y = 4(16) + 4(0) = 64
2. Maximize P = 3x + 2y
Subject to x + y ≤ 8
2x + y ≤ 13
x ≥ 0, y ≥ 0
Plot the constraints and the objective function Z, or P=3x+2y.
Push the objective function to the limit in the increase + direction permitted by the feasible region to find the maximum intersection.
Answer: Objective function is at a maximum at (5,3),
Z = 3x+2y = 3(5)+2(3) = 21
Answer:
Step-by-step explanation:
2x+5=-12
2x=-17
x=-8.5
Rewrite the limit as
Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get