Find the optimal crude oil allocation in the preceding example if the profit associated with fiber were cut in half, that is, fell to $.375 per square foot
what preceding example?
To find the optimal crude oil allocation when the profit associated with fiber is halved, we can use linear programming. Linear programming allows us to maximize or minimize an objective function while satisfying a set of linear constraints.
Let's assume there are two variables:
x = crude oil allocation in barrels
y = fiber allocation in square feet
The objective function represents the profit we want to maximize:
Profit = 0.5y + 0.25x
Now let's set up the constraints:
1. Availability of crude oil: 0.5x ≤ 100
2. Availability of fiber: y ≤ 80
3. Production limit: x + 2y ≤ 160
Since we are looking for the optimal allocation, we need to maximize the objective function while satisfying the constraints.
There are various methods to solve linear programming problems, such as the graphical method or the simplex method. Here, I'll use the graphical method for simplicity.
1. Plot the feasible region:
Graph the inequality constraints on a coordinate plane to determine the feasible region. Shade the region that satisfies all the constraints.
2. Identify the corner points:
The corner points of the feasible region are the vertices of the shaded area.
3. Evaluate the objective function at each corner point:
Compute the profit at each corner point by plugging in the x and y values into the objective function.
4. Determine the optimal solution:
The optimal solution is the corner point with the highest profit.
By following these steps, we can find the optimal crude oil allocation when the profit associated with fiber is halved.