Answer
The required numbers are 24 British Planes and 20 American Planes.
Work Step by Step
Let the number of American planes denoted by y and number of British planes by x. The equation from the first constraint is \[x+y\le 44\]. The equation from the second constraint is \[16y+8x=512\]. The equation from the third constraint is \[9000y+5000x=300000\]. By combining these three equations we could see the corners of the graph. Let the total number of British planes which is the objective function be denoted by\[z\]. The equation for objective function is \[z=y+x\].
The maximum or minimum of the objective function occur at the one or more of the corner points.
