Question 3 [25 pts] Consider the following nonlinear programming problem: The profit function z is: z = vp -cf-vcv

Where, v denotes volume to be produced, p is the selling price of one unit of product, cf is the fixed cost, cv is the variable cost per product.

The volume function is: v= 9200 56.7p Cost parameters are: cf = 30000 and cv = 24.

Note that this problem is very similar to the problem in our Nonlinear Programming class notes on Sakai.

a. [15 pts] Using the given variables and parameters, write down the z function in terms of p.