# Determine the maximum profit

Please help with the following solution regarding production and maximum provide. Provide step by step calculations in the completed solution.

A firm produces two goods 1 and 2 and has the following cost function

C = 10Q1 + Q1Q2 + 10Q2

Where Q1 and Q2 denote quantities of good 1 and 2. P1 and P2 denote the corresponding prices and the demand functions are:

P1 = 50 - Q1 + Q2

P2 = 30 + 2Q1 - Q2

Determine the maximum profit if the firm in total produces 15 units, that is if Q1 + Q2 = 15.

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#### Solution Preview

Problem: A firm produces two goods 1 and 2 and has the following cost function

C = 10Q1 + Q1Q2 + 10Q2

Where Q1 and Q2 denote quantities of good 1 and 2. P1 and P2 denote the corresponding prices and the demand functions are:

P1 = 50 - Q1 + Q2

P2 = 30 + 2Q1 - Q2

Determine the maximum profit if the firm in total ...

#### Solution Summary

This solution helps determine the maximum profit in this case of production given cost functions, demand function, and total production amount. Step by step calculations are provided.