a small business two types of computer, how many of each should they sell to make the most profit

Question

Netbooks cost £50 materials and £40 labour giving £70 profit, laptops cost £50 labour and £50 materials giving £110 profit. In any given month labour costs cannot be higher than £1350 and materials must not cost more than £1150.

 

How many of each type of computer should they sell each month to make the maximum profit

Answer 1

This is a linear programming problem.  Let x = the number of notebooks and y = the number of laptops.  The function to be optimized is the profit:

 

Profit = 70x + 110y

 

Your constraints on labor and materials are:

 

40x + 50y ≤ 1350

50x + 50y ≤ 1150

x ≥ 0

y ≥ 0

 

Graph the 4 inequalities.  The feasible zone - the section of the coordinate plane that contains solutions to all of the inequalities - is the region bounded by the inequalities.  The maximum profit lies at one of the vertices on the outside border.  Note the (x,y) coordinates of each vertex, then plug them into the Profit equation.  The (x,y) pair that gives the highest profit is the answer.