Philips Industries manufactures a certain product that can be sold directly to retail outlets or to Superior Company for further processing and eventual sale as a completely different product. The demand function for each of these markets is
Retail Outlets: P1=60-2Q1
Superior Company: P2=40-Q2
where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Phillips's total cost function for the manufacture of this product is TC=10+8(Q1+Q2)
Calculate the profit maximizing level of price and output it Phillips is required to charge the same price per unit in each market. What are Phillips's profits under this condition?