A company has trained five salespersons in the past three months, whom it wants to assign to three sales regions: North, West and South. It has been estimated that increases in sales (in lakhs of rupees) over the next year in each region, if each were allocated different number of salesmen, are as indicated below.

Use dynamic programming to determine which allocation would maximise the increase in sales.

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Region Salespersons North West South 0 0 0 0 1 61 36 66 2 86 61 86 34 106 91 96 121 126 116 5 136 166 146