MATH HELPPPPPPPPPP

Question

You are working in a firm that helps companies grow their businesses and maximize their incomes. Your team is assigned to an alcohol manufacturer. They can only produce two sizes of alcohol, 150 ml and 250 ml. Daily, they can produce up to 300 liters of alcohol. They noticed that for every P2 increase in their 150ml alcohol, the number of orders is reduced by 50 pieces and for every P5 increase in their 250ml alcohol, the number of orders is reduced by 40 pieces. How many 150 ml and 250ml alcohol do they need to produce and how much is the price of each kind to maximize their profit? Currently the price of 150 ml is P25 and the 250ml alcohol costs P40 each

Answer 1

The 150 ml case: 300/.150=2000

2n increases and 50n decreases.

For 2000 bottles,

(25+2n)(2000-50n)=0

50000-1250n+4000n-100n²=0

50000+2750n-100n²=0

^{Taking the derivative for maximization,}

^2750-200n=0

^{Solving for n,}

^{n or the maximizing price is $27.50.}

^{You can do the same with the 250ml. Then compare the profit form both.}