Feasible region ?

1 Answer
Apr 4, 2017

Answer:

See below.

Explanation:

Calling #p_c=52.5#, #p_s = 37.5#
and defining

#n_c = #number of cement bags
#n_s = #number of sand bags

the feasible quantities obey the restrictions

#{(n_c ge 16),(n_s ge 8),(n_c+n_s ge 105),(n_c+n_s le 248):}#

The weight function is

#W = n_c p_c+n_s p_s#

Follows a plot showing the feasible region superimposed with a level weight function representation. The level function representation is done drawing the successive lines in the plane #n_c,n_s# associated to a given total weight

The parallel lines are the plot of #W_i = n_cp_c+n_sp_s# with
#W_i={w_1,w_2,w_2,cdots,}#

In the plot can be observed to the bottom right the maximum weight point attained with #n_c=248, n_s = 8# and at the bottom left we have the minimum weight point attained at #n_s = 89, n_c=16#

The maximum weight is then

#W_(max)=248 xx 52.5+8 xx 37.5#

and the minimum

#W_(min)=16 xx 52.5+89 xx 37.5#

enter image source here