Answer to Question #255020 in Math for Boomie

Question

4.1 A motor company manufacture and sell cars and motorbikes. The cost of manufacturing x motorbikes and y cars is given by C(x, y) =100x² +100xy + 400y² . Each motorbike is sold for $36 000 and each car is sold for $180 000 Use Cramer’s rule to determine the number of motorbikes and the number of cars that should be manufactured and sold for a maximum profit II and determine the maximum profit II max .

4.2 Use the Jacobian to test for functional dependence between the cost and the revenue functions in 4.1.

4.3 One of the stationary points of the function f (x, y) = x⁴ + y⁴ − 2x² + 4xy − 2y² is ( √2,− √2 ) .

Use the Hessian to test whether the given point is a maximum, minimum or a saddle point.