Answer:
Obj Function, Max P=8w+16b
Subject to the Constraints
3w+2l≤80
4w+10b≤100
w≥6
b>0
Step-by-step explanation:
Let the number of Wren's birdhouse built=w
Let the number of bluebirds birdhouse built=b
Constraint:Labour
Each wren birdhouse takes 3 hours of labor.
Each bluebird house requires 2 hours of labor.
The craftsman has available 80 hours of labor
Formulated as an inequality:
3w+2l≤80
Constraint: Lumber
Each wren birdhouse requires 4 units of lumber.
Each bluebird birdhouse 10 units of lumber.
The craftsman has available 100 units of lumber
Formulated as an inequality:
4w+10b≤100
The craftsman wants to build at least 6 wren houses.
w≥6
Since he builds the two kinds of house, b>0 and w>0.
Objective Function
Wren houses profit $8 each and bluebird houses profit $16 each.
The Objective of the function is to make profit, so we maximize.
Obj Function, Max P=8w+16b
The linear programming problem is therefore stated below:
Obj Function, Max P=8w+16b
Subject to the Constraints
3w+2l≤80
4w+10b≤100
w≥6
b>0
in the denominator, so:![x^2-2x-3\neq0\\\\(x^2-2x+1)-4\neq0\\\\(x-1)^2-4\neq0\\\\(x-1)^2-2^2\neq0\qquad\qquad[\text{use }a^2-b^2=(a-b)(a+b)]\\\\(x-1-2)(x-1+2)\neq0\\\\ (x-3)(x+1)\neq0\\\\\boxed{x\neq3\qquad\wedge\qquad x\neq-1}](https://tex.z-dn.net/?f=x%5E2-2x-3%5Cneq0%5C%5C%5C%5C%28x%5E2-2x%2B1%29-4%5Cneq0%5C%5C%5C%5C%28x-1%29%5E2-4%5Cneq0%5C%5C%5C%5C%28x-1%29%5E2-2%5E2%5Cneq0%5Cqquad%5Cqquad%5B%5Ctext%7Buse%20%7Da%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29%5D%5C%5C%5C%5C%28x-1-2%29%28x-1%2B2%29%5Cneq0%5C%5C%5C%5C%0A%28x-3%29%28x%2B1%29%5Cneq0%5C%5C%5C%5C%5Cboxed%7Bx%5Cneq3%5Cqquad%5Cwedge%5Cqquad%20x%5Cneq-1%7D)
