A company is deciding whether to develop and launch a new product. Research and development costs are expected to be ksh$400,000$ and there is a $70\%$ chance that the product launch will be successful, and a $30\%$ chance that it will fail. If it is successful, the levels of expected profits and the probability of each occurring have been estimated as follows, depending on whether the product$$s popularity is high, medium or loW.

Probability Profits

High $0\mathrm{.}2$ ksh $500,000$ per annum for two years.

Medium $0\mathrm{.}5$ ksh $400,000$ per annum for two years.

Low $0\mathrm{.}3$ ksh $300,000$ per annum for two years.

If it is a failure, there is a $0\mathrm{.}6$ probability that the research and development work can be sold for ksh $50,000$ and a $0\mathrm{.}4$ probability that it will be worth nothing at all. Advice the management the best option to take.