The lifting force, $F$, exerted on an airplane wing varies jointly as the area, $A$, of the wing's surface and the square of the plane's velocity, $v$. The lift of a wing with an area of 160 square feet is 11,900 pounds when the plane is going at 200 miles per hour. Find the lifting force if the speed is 230 miles per hour. Round your answer to the nearest integer if necessary. Answer pounds

Step 1 ：Given that the lifting force, $F$, exerted on an airplane wing varies jointly as the area, $A$, of the wing's surface and the square of the plane's velocity, $v$. This relationship can be expressed as $F = kAv^2$, where $k$ is the constant of variation.

Step 2 ：We are given that the lifting force is 11,900 pounds when the area is 160 square feet and the velocity is 200 miles per hour. We can use these values to find the constant of variation, $k$. Substituting the given values into the equation, we get $11900 = k * 160 * 200^2$. Solving for $k$, we find that $k = 0.001859375$.

Step 3 ：Now we can use the value of $k$ to find the lifting force when the velocity is 230 miles per hour. The area remains the same at 160 square feet. Substituting these values into the equation, we get $F = 0.001859375 * 160 * 230^2$, which simplifies to $F = 15738$ pounds.

Step 4 ：Final Answer: The lifting force when the speed is 230 miles per hour is \(\boxed{15738}\) pounds.