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
