Answer to Question #294842 in Operations Research for musenga sichona

Question

A poultry farmer in Lufyanyama has obtained a loan from the Bank to boost his poultry business. He provides you with data to help him optimize the sales. The data is that Old hens can be bought for K20 each but young one cost K50 each. The old hens lay 30 eggs per week, and young ones 50 eggs per week, each egg being worth30ngwee. A hen cost K10 per week to feed. If a person has only K800 to spend on hens, how many of each kind should he buy to get a profit of more than K600 per week assuming that he can’t house more than 200 hens?

a) Formulate the problem as a linear programming model [8 Marks]

b) Using the Big M – method, how many hens should he buy of each kind to maximize the profit per week [13 Marks]

c) Identify the binding and non-binding constraints and justify your choice [4 Marks]