A company must determine how much of its £190,000 advertising and promotional budget should be spent in the following media: television, radio, magazines, and prize promotion. Each pound spent on television advertising increases sales by £24; each pound spent on radio and magazine ads results in half of that return, and prize promotion returns £11 in sales for each pound invested.
Television advertising cannot exceed a third of the total budget, and total radio advertising must be at least 30% of the total TV advertising. At least £22,000 must be spent on magazine ads, and no more than £22,000 may be spent on the prize promotion. What is the maximal total increase in sales that can be achieved by optimal allocation of the funds in the advertisements?