Question: John is interested in expanding his firm. After careful consideration, he has determined three areas in which he might invest additional funds during the next four-year period:

(1) product research and development,

(2) manufacturing operations improvements, and

(3) advertising and sales promotion.

He has £500000 available for investment in the firm. He can invest in its advertising and sales promotion program every year, and each pound invested in this manner is expected to yield a return of the amount invested plus 15% yearly.He can invest in manufacturing operations improvements at the beginning of year 1 and year 3, with an expected return of the amount invested plus 32% (at the end of each two-year period). An investment in product research and development, which is only available at the beginning of year 1, would be for a three year period only, with an expected return of the investment plus 40% (at the end of the three-year period). To diversify the total initial investment, he wishes to include the requirement that at least £25000 must be invested on the advertising and sales promotion program, at least £40000 on manufacturing operations improvements, and at least £50000 on product research and development initially (at the beginning of the first year). What is the maximum final cash value (i.e. initial capital plus profits earned) that can be achieved at the end of the four-year period by implementing an optimal investment strategy? (Please notice that the returns can be reinvested in any alternative available.)