A company can advertise its product by using a local radio and TV stations. Its budget limits the advertisement expenditures to $1000 a month. Each minute of radio advertisement costs $5, and each minute of TV advertisement costs $100. The company would like to use the radio at least twice as much as the TV. Past experience shows that each minute of TV advertisement will usually generate 25 times as many sales as each minute of radio advertisement.

(a) Required to model the problem of determining the optimum allocation of the monthly budget to radio and TV advertisements as a linear programming problem.

(10 marks)

(b) Solve the model by graphical method to find the optimal allocation.

(15 marks)

(c) Find the shadow prices of the constraints and explain their economic implications.

(10 marks)

(d) Find the range of values for the objective function coefficients so that the optimal solution arrived at (b) remains optimal. (10 marks)