A monopolistic producer of two goods, G1 and G2, has a total cost function

TC = 5Q 1 + 10Q 2

where Q 1 and Q 2 denote the quantities of G1 and G2, respectively. If P 1 and P 2 denote

the corresponding prices, then the demand equations are

P 1 = 50 Q 1 Q 2

P 2 = 100 Q 1 4Q 2

Use Lagrange Multiplier to find the maximum profit if the firm's total costs are fixed at

$100. Estimate the new optimal profit if total costs rise to $101.