Question

John sells notebooks and pencils and notebooks. In a week he can sell between 400 and 500 pencils and between 150 and 200 notebooks but not more than 650 items altogether. Each pencil costs P18 and sells for P25 while each notebook costs P28 and sells for P45. How many of each type should he get to gain the maximum profit per week? 1. Formulate the problem above as a linear programming problem with objective function and constraints . Start by defining the decision variables and the profit function

Answer 1

$\text{Let $x_1=$no of pencils}\\\text{Let $x_2=$no of notebooks}\\\text{The profit function is given by}\\z=7x_1+17x_2 \\\text{Note that P7 and P17 are profits made from selling pencils and notebooks respectively} \\\text{The constraints are as follows;} \\400\leq x_1 \leq 500 \\ 150 \leq x_2 \leq 200\\x_1+x_2 \leq 650 \\\text{with $x_1$ and $x_2$ non-negative}$