A monopolistic producer of two goods, G₁ and G₂, has a total cost function
TC = 5Q₁ + 10Q₂
where Q₁ and Q₂ denote the quantities of G₁ and G₂, respectively. If P₁ and P₂ denote the corresponding prices, then the demand equations are
P₁ = 50 − Q₁ − Q₂
P₂ = 100 − Q₁ − 4Q₂
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.