Intel and AMD, the primary producers of computer central processing units (CPUs), compete with one another in the mid-range chip category (among other categories). Assume that global demand for...

Intel and AMD, the primary producers of computer central processing units (CPUs), compete with one another in the mid-range chip category (among other categories). Assume that global demand for mid-range chips depends on the quantity that the two firms make, so that the price (in dollars) for mid-range chips is given by
  and where the quantities are measured in millions. Each midrange chip costs Intel $60 to produce. AMD’s production process is more streamlined; each chip costs them only $48 to produce.

(a) Write the profit function for each firm in terms of q_Intel
and q_AMD. Find each firm’s best-response rule.

(b) Find the Nash equilibrium price, quantity, and profit for each firm.

(c) (Optional) Suppose Intel acquires AMD, so that it now has two separate divisions with two different production costs. The merged firm wishes to maximize total profits from the two divisions. How many chips should each division produce? What is the market price and the total profit to the firm?