Linear Programming

A dressmaker can make a maximum of 20 dresses per week. She can make either silk dresses or cotton dresses. The material for a cotton dress costs R100 per dress and R200 per silk dress. She has R3000 to spend on the material. She needs to make at least 5 of each dress. Let X be the number of cotton dresses and Y be the number of silk dresses. a) Write down the constraint inequalities. b) Represent the constraints on a graph and shade the feasible region. c) The profit on a cotton dress is R40 and R50 on a silk dress d) Determine the amount of each dress to make a maximum profit. e) Calculate the maximum profit.