Step $1$: Calculate the expected value for each strategy.

Expected Value Formula:

EV$=($P$1$Payoff$$in$$state$1)+($P$2$Payoff$$in$$state$2)+($P$3$Payoff$$in$$state$3)\backslash$text$\{$EV$\}=($P$\_1\backslash$times $\backslash$text$\{$Payoff in state $1\})+($P$\_2\backslash$times $\backslash$text$\{$Payoff in state $2\})+($P$\_3\backslash$times $\backslash$text$\{$Payoff in state $3\})$EV$=($P$1$Payoff$$in$$state$1)+($P$2$Payoff$$in$$state$2)+($P$3$Payoff$$in$$state$3)$

Strategy S$1$:

EVS$1=(0\mathrm{.}3050$K$)+(0\mathrm{.}5030$K$)+(0\mathrm{.}2070$K$)\backslash$text$\{$EV$\}\_\{$S$1\}=(0\mathrm{.}30\backslash$times $-50$K$)+(0\mathrm{.}50\backslash$times $30$K$)+(0\mathrm{.}20\backslash$times $70$K$)$EVS$1=(0\mathrm{.}3050$K$)+(0\mathrm{.}5030$K$)+(0\mathrm{.}2070$K$)$

Strategy S$2$:

EVS$2=(0\mathrm{.}3080$K$)+(0\mathrm{.}5020$K$)+(0\mathrm{.}2040$K$)\backslash$text$\{$EV$\}\_\{$S$2\}=(0\mathrm{.}30\backslash$times $-80$K$)+(0\mathrm{.}50\backslash$times $20$K$)+(0\mathrm{.}20\backslash$times $40$K$)$EVS$2=(0\mathrm{.}3080$K$)+(0\mathrm{.}5020$K$)+(0\mathrm{.}2040$K$)$

Strategy S$3$:

EVS$3=(0\mathrm{.}3070$K$)+(0\mathrm{.}500)+(0\mathrm{.}2050$K$)\backslash$text$\{$EV$\}\_\{$S$3\}=(0\mathrm{.}30\backslash$times $-70$K$)+(0\mathrm{.}50\backslash$times $0)+(0\mathrm{.}20\backslash$times $50$K$)$EVS$3=(0\mathrm{.}3070$K$)+(0\mathrm{.}500)+(0\mathrm{.}2050$K$)$

Strategy S$4$:

EVS$4=(0\mathrm{.}30200$K$)+(0\mathrm{.}5050$K$)+(0\mathrm{.}20150$K$)\backslash$text$\{$EV$\}\_\{$S$4\}=(0\mathrm{.}30\backslash$times $-200$K$)+(0\mathrm{.}50\backslash$times $-50$K$)+(0\mathrm{.}20\backslash$times $150$K$)$EVS$4=(0\mathrm{.}30200$K$)+(0\mathrm{.}5050$K$)+(0\mathrm{.}20150$K$)$

Strategy S$5$:

EVS$5=(0\mathrm{.}300)+(0\mathrm{.}500)+(0\mathrm{.}200)=0\backslash$text$\{$EV$\}\_\{$S$5\}=(0\mathrm{.}30\backslash$times $0)+(0\mathrm{.}50\backslash$times $0)+(0\mathrm{.}20\backslash$times $0)=0$EVS$5=(0\mathrm{.}300)+(0\mathrm{.}500)+(0\mathrm{.}200)=0$

Let's compute these expected values to identify the best strategy.

Expected Values for Each Strategy:

S$1$: $$14,000$

S$2$: $$-6,000$

S$3$: $$-11,000$

S$4$: $$-55,000$

S$5$: $$0$

Analysis:

Best Strategy $($Expected Value Approach$)$: The strategy with the highest expected value is S$1$ with an expected profit of $$14,000.$ Therefore, S$1$ should be chosen if the goal is to maximize expected profit.

Go$-$for$-$Broke Attitude: A go$-$for$-$broke manager would choose the strategy with the highest potential payoff regardless of risk. The highest potential payoff is S$4($Total Success $=$ $$150,000).$

Pessimistic Approach $($Without S$5)$: A pessimist would consider the worst$-$case scenario for each strategy and choose the one with the least negative impact:

Worst outcomes:

S$1$: $$-50$KS$2$: $$-80$KS$3$: $$-70$KS$4$: $$-200$K

The least negative worst$-$case outcome is S$1$ with a potential loss of $$-50$K$.$

Pessimistic Approach $($With S$5)$: If S$5$ were an option, a pessimist would choose it$,$ as it guarantees a payoff of $$0$ with no risk of loss.

Final Answers:

Part a: Strategy S$1$ should be taken based on expected value.

Part b: The go$-$for$-$broke choice would be S$4.$

Part c: A pessimist without S$5$ would choose S$1.$

Part d: With S$5$ available, a pessimist would choose S$5.$