Consider the following constrained maximization problem: maximize y x + 5 Inx subject to k-0, = where k is a constant that can be assigned any specific value.

a. Show that if 10, this problem can be solved as one involving only equality constraints.

b. Show that solving this problem for k = 4 requires that x = -1.

c. If the x's in this problem must be nonnegative, what is the optimal solution when k = 4?

d. What is the solution for this problem when k = 20? What do you conclude by comparing this solution to the solution for part (a)? Note: This problem involves what is called a "quasi-linear function." Such functions provide important examples of some types of behavior in consumer theory-as we shall see.