Hello,

to a). I don't know a Management Scientist but I can give you a solution.

I use x for your A and I use y for your B.

1A + 1B is less than or equal to 10:

3A + 1B is less than or equal to 24:

1A + 2B is less than or equal to 16:

A, B is greater than or equal to 0:

I sketched the 3 straight lines which are the borders of the half-planes. You get an irregular pentagon (hmm... don't forget we are talking about math). The graph of the objective function must pass at least through one point of this pentagon.

Max = 3A + 2B: . That means the y-intercept is . The larger the y-intercept the larger is Max. If the graph of the objective function passes through B(7, 3) then the y-intercept will be the largest.

Calculate the equation of the obj. function (sketched in red):

. Therefore .

to b).

Max = 5A + 2B: . That means the y-intercept is . The larger the y-intercept the larger is Max. If the graph of the objective function passes through B(7, 3) then the y-intercept will be the largest.

Calculate the equation of the obj. function (sketched in green):

. Therefore .

to c).

Max = 3A + 4B: . That means the y-intercept is . The larger the y-intercept the larger is Max. If the graph of the objective function passes through A(4, 3) then the y-intercept will be the largest.

Calculate the equation of the obj. function (sketched in blue):

. Therefore .