Mathematics

Problem

A feasible region

R

is the triangle with vertices

(0,0)

(6,0)

and

(0,4)

. It arises from the constraints

x \ge 0,\; y \ge 0,\; x + k y \le c,\quad k > 0,\; c > 0

Another feasible region

S

is the triangle with vertices

(0,0)

(8,0)

and

(0,4)

obtained by modifying exactly one element of the same set of constraints. a. (i) Using the given vertices of

R

, determine the values of

k

and

c

. b. (ii) Identify precisely which single parameter (either

k

c

) must be changed, and state its new value, so that the feasible region becomes

S

. c. (iii) Justify, without plotting, why altering only this parameter yields the stated shift in the vertex on the x-axis while leaving the other two vertices unchanged.

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