Personal Mini Warehouses is planning to expand its successful Nashua business into Lowell. In doing so, the company must determine how many storage rooms of each size to build. The problem has been formulated as a linear program (LP), as follows:

Where x1 is the number of large spaces developed, and x2 is the number of small spaces developed. where xi is the number of large spaces developed, and xt is the number of small spaces developed.
a). The constraint boundaries are shown in the graph below. Different regions are labeled A through G. Which region or regions correspond to the feasible region of this problem.
b). Possible corner points for this problem are labeled [ 1 ] through [8] in the graph below. Which one is the optimal corner point? Justify you response with calculations and/or pictures.

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maximize Z= 60x1 + 50x: subject to: 2x1 (monthly eamings) 4x 3 400 (advertising budget) 100x, + 60x, < 8000 (square footage required) 60 (rental limit expected) X, X & 200 180 160 1400 120 1002 80 60 40 20 X1 20 40 60 80 100 120 140 160 180 200 220 B.