3. A dairy produces whole milk and skim milk in quantities x and y gallons, respectively. Suppose that the price of whole milk is p(x) = 100 - x and that of skim milk is q(y)= 100 - y and assume that (, ) = 2 + + 2 is the joint-cost function of the commodities. What should x and y be to maximize profit?

4. A T-shirt shop carries two competing shirts, one endorsed by Michael Jordan and the other by Shaq O'Neal. The owner of the store can obtain both types at a cost of $2 per shirt and estimates that if Jordan shirts are sold for x dollars apiece and O'Neal shirts for y dollars apiece, consumers will buy approximately 40 - 50x + 40y Jordan shirts and 20 + 60x - 70y O'Neal shirts each day. How should the owner price the shirts in order to generate the largest possible profit?