Find the greatest value of x3y4 if 2x plus 3y7 and x0y0?

Answer 1

To maximize ( x^3y^4 ) given the constraint ( 2x + 3y = 7 ) and ( x \geq 0, y \geq 0 ), we can use the method of Lagrange multipliers or substitute ( y ) in terms of ( x ). From the equation, express ( y ) as ( y = \frac{7 - 2x}{3} ). Substituting this into ( x^3y^4 ) will yield a function of ( x ) that can be maximized within the feasible region defined by the constraints. Solving this will give the maximum value of ( x^3y^4 ).