Help w/ Inequalities Question (34)?

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Help w/ Inequalities Question (34)?
a graph should be drawn as well

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Answer 1 · 2017-11-07T15:04:27

See below.

Calling

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

we have the restrictions

#8 n_X +2 n_Y ge 16#
#1 n_X + 1 n_Y ge 5#
#2 n_X +7 n_Y ge 20#

and the objective function to be minimized

#f = 15 n_X + 30 n_Y#

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

#f_(min) = 15 n_(X_min)+30 n_(Y_min)# in red

The minimum point is #n_(X_min) = 3, n_(Y_min) = 2# with #f_min = 105#

enter image source here