A company makes two products, A and B, from the same materials and needs to decide how to allocate limited resources to the production of A and B. If it produces x units of A and y units of B, then x and y satisfy the equation
36x2 + 25y2 = 90,000

Each point (x, y) on this curve represents a production schedule specifying that x units of A and y units of B should be made. If each unit of A yields a profit of $6 and each unit of B yields a profit of $10, then the profit function is
P(x, y) = 6x + 10y.
Determine the production schedule that maximizes profit.

Question

A company makes two products, A and B, from the same materials and needs to decide how to allocate limited resources to the production of A and B. If it produces x units of A and y units of B, then x and y satisfy the equation
36x2 + 25y2 = 90,000

Each point (x, y) on this curve represents a production schedule specifying that x units of A and y units of B should be made. If each unit of A yields a profit of $6 and each unit of B yields a profit of $10, then the profit function is 
P(x, y) = 6x + 10y.
 Determine the production schedule that maximizes profit.

anonymous · Answer

A solution using two Mathematica 9 methods is attached.