The following figure shows a feasible region of a linear programming task with variables 𝑥ଵ

on the horizontal axis and 𝑥ଶ on the vertical axis. Non-negative constraints are also assumed but are not “coloured” in the figure. There are also coordinates of constraints’ intersections with the axis:

a) How many feasible solutions does this task have?
b) How many basic feasible solutions (candidates for optimal solutions) does it have?
c) Calculate the coordinates of point A, show your calculations (reading from the picture will be not evaluated).
d) Assume that A is the optimal point of the task and the optimal value of the minimizing objective function is 𝑧 = 15,6. Find any objective function for which the previous sentence is true.