Consider the following system of inequalities.

${x}_{1}-{x}_{2}\le 3\phantom{\rule{0ex}{0ex}}{x}_{2}-{x}_{3}\le -2,\phantom{\rule{0ex}{0ex}}{x}_{3}-{x}_{4}\le 10,\phantom{\rule{0ex}{0ex}}{x}_{4}-{x}_{2}\le \alpha ,\phantom{\rule{0ex}{0ex}}{x}_{4}-{x}_{3}\le -4,$

where $\alpha $ is a real number. A value for α for which the system has a solution is

(a) −16,

(b)−12,

(c)−10,

(d) None.

${x}_{1}-{x}_{2}\le 3\phantom{\rule{0ex}{0ex}}{x}_{2}-{x}_{3}\le -2,\phantom{\rule{0ex}{0ex}}{x}_{3}-{x}_{4}\le 10,\phantom{\rule{0ex}{0ex}}{x}_{4}-{x}_{2}\le \alpha ,\phantom{\rule{0ex}{0ex}}{x}_{4}-{x}_{3}\le -4,$

where $\alpha $ is a real number. A value for α for which the system has a solution is

(a) −16,

(b)−12,

(c)−10,

(d) None.