How do you know when to use Linear Programming to solve a word problem?

1 Answer
Oct 19, 2017

Please see below.

Explanation:

Linear programming is a simple technique where we depict complex relationships through linear relations. These relations are constraints which put restrictions on values of the output, which are non-negative i.e. zero or positive. The results in such cases are generally located at points and then we find the most optimal point based on , at which the desired objective, which is again a linear relation among decision variables and is either maximised or minimised.

Hence, we use Linear Programming to solve a word problem when (i) we have linear relations; and (ii) certain function has to be maximized or minimized.

For example, let us have available #x# hours of labour and #y# cubic feet of wood, which we can use to make either tables or chair. A chair requires #a_1# hours of labour and #a_2# cubic feet of wood and a table requires #b_1# hours of labour and #b_2# cubic feet of wood. We have a profit of #p_a# on chair and #p_b# on table. How can we maximise profits.

Let the result be #n_a# chairs and #n_b# tables. So our constraints are

#n_axxa_1+n_bxxb_1 <= x#
#n_axxa_2+n_bxxb_2 <= y#

We are to maximise #n_axxp_a+n_bxxp_b#

and non-negative outputs are #n_a# and #n_b#.