Help w/ Inequalities Question (33)?

Help w/ Inequalities Question (33)?
a graph should be drawn as well
enter image source here

1 Answer
Nov 7, 2017

See below.

Explanation:

Calling

#n_X = # number of brand #X# bags
#n_Y = # number of brand #Y# bags.

we have the restrictions

#2 n_X +1 n_Y ge 12#
#2 n_X + 9n_Y ge 36#
#2 n_X +3 n_Y ge 24#

and the objective function to be minimized

#f = 25 n_X + 20 n_Y#

Attached the feasible region in light blue, and the situation for the solution line

#f_(min) = 25 n_(X_min)+20 n_(Y_min)# in red

The minimum point is #n_(X_min) = 3, n_(Y_min) = 6# with #f_min = 195#

enter image source here