Feasible region ?

1 Answer
Cesareo R.
Apr 4, 2017

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

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