Problem $3(15\%)$

There are currently two modes of operation under consideration:

Mode B implies a more selective blasting pattern than Mode A; this ultimately leads to a slightly

lower blasting cost, but a considerably slower mining rate. Moreover, Mode A implies higher

comminution costs, as the ore is diluted with low grade material.

a$)$ Implement and solve a linear program to determine the most cost effective application of

modes A and B to excavate $18000t$ of rock in $96$ hours, considering drilling$-$and$-$blasting,

loading$-$and$-$hauling and comminution; consider the tonnages processed through modes A

and $B$ to be the decision variables, denoted $m_A$ and $m_B,$ respectively.

b$)$ Consider the formulation of part a$),$ and use the $18000t$ constraint to eliminate the $m_B$

variable, hence reducing the problem to a single variable $m_A.$ Proceed to solve this one$-$

variable linear program, without the use of Solver, and ensure that the result is consistent

with a$).$