A certain company offers two products (a, b, measured in thousands of units). Their respective demand equations are: \(4a+p_1=14\) and \(2b + p_2 = 24\) where \(p_1\), \(p_2\) stand for respectively- the selling price per unit of each product. The overall cost is given by \(a^ 2 + 5ab + b ^ 2\) Study the maximum profit. (2.5 points)
To study the maximum profit for the given company, we need to:
1. Define the profit function
a, b: quantities sold (in thousands)
\(p_1, p_2\): prices per unit of products a and b
2. From demand equation s, solve for price as a function of quantity:
Given:
