i need help with creating the decision tree in excel: Acme Toys has developed a new product$$the Captain Miller Action Figure $($CMAF$).$ They are now deciding how to market the doll.

One option is to immediately ramp up production and launch an ad campaign throughout the state of Oregon. This option would cost $$60,000.$ Based on past experience, new action figures either take off and do well, or fail miserably. Hence, they predict one of two possible outcomes$$ total sales of $20,000$ units or total sales of only $4,000$ units. The net profit per unit sold is $$5.$

Another option is to first test market the product in Bend before deciding whether to sell statewide. The test market would require less capital for the production run, and a much smaller ad campaign. Again, they predict one of two possible outcomes for Bend. The product will either do well $($sell $500$ units$)$ or do poorly $($sell $100$ units$).$ The cost for this option is estimated to be $$1,000.$ The net profit per unit sold is $$5$ for the test market as well. Once the test market is complete, Acme Toys would then use these results to help decide whether to market the toy statewide.

Acme Toys has test marketed similar toys in the Bend market $50$ times in the past, with the results shown in the table below. Since Acme Toys thinks CMAF is similar to these other toys, they plan to estimate the probabilities of the various outcomes based on these historical results. For example, ignoring the test$-$market results, $30$ out of $50$ of the previous toys sold well statewide, so without a test market, they estimate a $60\%$ probability for CMAF to sell well statewide. If a test market is done, these same data should be used to estimate the probabilities of the various outcomes.

$|$ Sells Well Statewide $|$ Sells Poorly Statewide $|$

$|------------------------|------------------------|$

$|$ Tests Well in Bend $|20|5|$

$|$ Tests Poorly in Bend $|10|15|$

There is a complication with the Bend test market option, however. A rival toy manufacturer is rumored to be considering the development of a Commander Smith Action Figure $($CSAF$).$ After doing the test market in Bend, if Acme Toys decides to go ahead and ramp up production and market throughout the state, the cost of doing so would still be $$60,000.$ However, the sales prospects depend upon whether CSAF has been introduced into the market or not. If CSAF has not entered the market, then the sales prospects will be the same as before $($i$.$e$.,20,000$ units if CMAF does well, or $4,000$ units if CMAF does poorly, on top of any units sold in the test market$).$ However, if CSAF has entered the market, the increased competition will diminish sales of CMAF. In particular, they expect to sell $10,000$ units if CMAF does well, and $2,000$ units if it does poorly, on top of any units sold in the test market. Note that the probability of CMAF doing well or doing poorly is not affected by CSAF, just the final sales totals of each possibility. If a test market is done, there is a $20\%$ chance that CSAF will enter during the test market $($before it completes$).$ On the other hand, if Acme Toys markets CMAF immediately, they are guaranteed to beat CSAF to market, thus making CSAF a non$-$factor.

a$.$ Use TreePlan to develop a decision tree to help Acme Toys decide the best course of action and the expected payoff. In words below the tree, state the best course of action assuming your goal is to maximize the expected payoff.

b$.$ Now suppose Acme Toys is uncertain of the probability that CSAF will enter the market before the end of the test market in Bend would be completed $($if it were done$).$ How does the expected payoff vary as the probability that CSAF would enter the market changes? On the same worksheet used for part a$,$ generate a data table that shows how the expected payoff and the initial decision change as the probability that CSAF enters varies from $0\%$ to $100\%($at $10\%$ increments$).$ At what probability does the decision change?