$10.$ A dynamic random access memory $($DRAM$)$ factory can produce $100,000$ chips per month at a unit cost of $\backslash (\backslash$$ $4\mathrm{.}00\backslash ).$ The current DRAM spot price is $\backslash (\backslash$$ $5\mathrm{.}50\backslash ).$ It can change by a factor of $\backslash ($ U$=1\mathrm{.}2\backslash )$ or $\backslash ($ D$=1/$ U $\backslash )$ each month and its risk$-$adjusted expected monthly growth factor is $\backslash ($ K$=1\mathrm{.}01\backslash ).$ The risk$-$free interest rate is $\backslash (1\backslash \%\backslash )$ per year. Use the dynamic programming approach to estimate the current market value of the factory's cash flows from one to six months from now, inclusive, assuming that the firm produces DRAM chips when and only when the spot price exceeds the marginal cost of production.