MathDB

Let

S

be the solid in three-dimensional space consisting of all points

(x,y,z)

satisfying the following six simultaneous conditions:

x,y,z \geq 0, \;\; x+y+z\leq 11, \;\; 2x+4y+3z \leq 36, \;\; 2x+3z \leq 44.

a) Determine the number

V

of vertices of

S.

b) Determine the number

E

of edges of

S.

c) Sketch in the

bc

-plane the set of points

(b, c)

such that

(2,5,4)

is one of the points

(x, y, z)

at which the linear function

bx + cy + z

assumes its maximum value on

S.

B2