(a) 50 radio and 30 TV ads giving a total rating of 28000 (b) Radio and budget constraints binding. Shadow price of radio ads constraint is 50 so If radio ads increased by 50 then extra rating would be 50 x 50 = 2500 (c) Can’t reduce TV ads rating. 8. (a) Let = Amount invested in government x1 Let = Amount invested in corporate bonds x2 Let = Amount invested in FTSE 100 stocks x3 Let = Amount invested in Aim stocks x4 Max .04x1 + .05x2 + .06x3 + .08x4 + .03(550000 - - - - x1 x2 x3 x4) i.e. Max 16500 + .01x1 + .02x2 + .03x3 + .05x4 s.t + + + 550 000 x1 x2 x3 x4 ≤ 50 000 x2 ≥ + + 300 000 x2 x3 x4 ≤ + - - 0 x1 x2 x3 x4 ≤ + + x3 - 3x4 0 x1 x2 ≥ , , , 0 x1 x2 x3 x4 ≥
(a) 50 radio and 30 TV ads giving a total rating of 28000 (b) Radio and budget constraints binding. Shadow price of radio ads constraint is 50 so If radio ads increased by 50 then extra rating would be 50 x 50 = 2500 (c) Can’t reduce TV ads rating. 8. (a) Let x1 = Amount invested in government Let x2 = Amount invested in corporate bonds Let x3 = Amount invested in FTSE 100 stocks Let x4 = Amount invested in Aim stocks Max .04x1 + .05x2 + .06x3 + .08x4 + .03(550000 - x1 - x2 - x3 - x4) i.e. Max 16500 + .01x1 + .02x2 + .03x3 + .05x4 s.t x1 + x2 + x3 + x4 ≤ 550 000 x2 ≥ 50 000 x2 + x3 + x4 ≤ 300 000 x1 + x2 - x3 - x4 ≤ 0 x1 + x2 + x3 - 3x4 ≥ 0 x1 , x2 , x3 , x4 ≥ 0
Solutions%20Manual.docx