A two product monopoly faces the following demand and cost functions:

?(?_1)^d [not an exponent]= 40 ? 2?_1 ? ?_2

??_2^d = 35 ? ?_1 ? ?_2

?? = ?_1^2 + 2?_2^2 + 10

a. Find the pair of prices, p_1 and p_2, that satisfy the first-order necessary conditions for a local maximum of the profit function: ?(?_1, ?_2 ) = ?_1?_1^? (?_1,?_2) + ?_2?_2^? (?_1,?_2) ? ((?_1^? (?_1,?_2))^2 + 2(?_2^? (?_1,?_

6. A two product monopoly faces the following demand and cost functions: a. C. ' qf=40-2p1pz - q=35p1p2 - c=qf+2q+10 Find the pair of prices, p1 and P2, that satisfy the first-order necessary conditions for a local maximum of the profit function: 7:091, p2) = plqplpz) + p2q(p1,p2) (613101.992 + 26:? (p1.p2)2 + 10) Confirm that the second-order, sufficient condition for a local maximum is met at that pair of prices. Can you conclude that the local maximum you have identied is also a global maximum? Explain. How much of each product will be produced and sold? What will the firm's profit be