MTH320: Homogeneous,Stating the Degree. State and Fully Verify the Euler’s Theorem Mathematical Methods Assignment, SUSS, Singapore

1.Use the definition of the homogenous function to show the following function is homogeneous, stating the degree. State and fully verify the Euler’s Theorem in this case

2. The function f is homogeneous. Determine the values of a, c, d and h

3. The function f is defined for all real numbers x and y byFind and classify the stationary points of  f

When a consumer has positive quantities, x and y, of apples and oranges respectively, his utility is given by

Given that each apple costs $4 and each orange costs $1, find the quantities, x* and y*, that will maximise his utility given that he spends $M on apples and oranges. Also find the corresponding value of the Lagrange multiplier, λ*, giving your answer in the simplest possible form.