Question 1 (a) Blitz Beer has allotted $10,000 for radio advertising in Gotham City and must determine the placement of spot advertisements that will maximize increased sales. Top 40 stations attract a heavier beer-drinking audience than golden-oldie stations do, but top- 40 stations also charge more for each spot. The following data apply. Station Cost per spot Sales increase per spot Spots available Format A $100 $300 30 Top-40 B $50 $120 unlimited Golden-oldie C $75 $150 unlimited Golden-oldie D $150 $400 Top-40 40 At least 30% of the spots must be placed with golden-oldie stations. Formulate Blitz's problem as a linear programming problem. (No need to solve it.) (15 marks) (b) (i) Find the optimal solution of the following Linear Programming problem, using Simplex method. Maximize-X, + 3x, + 2 x; subject to 3x; - x2 + 2xy s7 -2x, + 3x, s 12 4x, +3 x, + 6x; s 15 X, X, X; 20 (1) (2) (3) (26 marks) (ii) Which of the constraints (1) - (3) are binging, and which of them are non-binding? (3 marks) (iii) Write down the shadow prices of constraints (1) - (3). (3 marks) (iv) Write down the reduced costs for x,, x, and xy