Perform an analysis to assist in deciding how much of two products to
produce to maximize the profit. The total profit associated with producing a units of product a and b units product b is given as a single function that is given below:
𝑃𝑃 (𝑎𝑎 , 𝑏𝑏 ) = 0.2𝑎𝑎 2 − 1.1𝑎𝑎 + 12√𝑏𝑏 − 2.5𝑏𝑏
where
P is the total profit ($)
a is the amount of product a to produce (tons)
b is the amount of product b to produce (tons) The coefficients in front of each term (i.e., 0.2, 1.1, 12 and 2.5) convert the terms into US
dollars.
Find the values of a and b that maximize C.