Question

Feasible region ?

Answer 1

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`