Inequalities

Question

Upon completing the construction of his house,Mr Charles discovers that 100 sq.ft of plywood scrap and 80 sq.ft of white pine scrap are in usable form for the construction of tables and book cases.It takes 16 sq.ft of plywood and 8 sq.ft of white pine to make a table, 12 sq.ft of plywood and 16 sq.ft of white pine wood are required to construct a book case. Identify the inequalities that form the constraints of availability of plywood and white pine. Provide advice on how the inequalities could be solved.

Answer 1

Let the # of tables to be constructed be t

and the number of bookcases           be b

 

From the above information

 

constraint on plywood; 16t + 12b <= 100

 

constraint on pine;        8t + 16b <= 80

 

                                             t >= 0

                                             b >= 0

 

A graphical solution is the simplest way to go, or you could solve two simultaneous linear equations

 

Graphical

Plot two linear graphs of t against b

 

observe the inequalities and shade the areas below both lines (bounded by the first quadrant)

 

Wherever the shading coincides indicate the areas of the solution set

 

The vertex of this solution set would be your optimal solution

 

Solving linear simultaneous equations give ; number of tables (t) = 4; and number of bookcases (b) = 3