A particular company is considering bidding on a contract for a new office building complex. The figure below shows the decision tree prepared by one of the company's analysts. At node $1,$ the company must decide whether to bid on the contract. The cost of preparing the bid is $$220,000.$ The upper branch from node $2$ shows that the company has a $0\mathrm{.}8$ probability of winning the contract if it submits a bid. If the company wins the bid, it will have to pay $$2,000,000$ to become a partner in the project. Node $3$ shows that the company will then consider doing a market research study to forecast demand for the office units prior to beginning construction. The cost of this study is $$130,000.$ Node $4$ is a chance node showing the possible outcomes of the market research study. Nodes $5,6,$ and $7$ are similar in that they are the decision nodes for the company to either build the office complex or sell the rights in the project to another developer. The decision to build the complex will result in an income of $$5,000,000$ if demand is high and $$3,000,000$ if demand is moderate. If the company chooses to sell its rights in the project to another developer, income from the sale is estimated to be $$3,500,000.$ The probabilities shown at nodes $4,8,$ and $9$ are based on the projected outcomes of the market research study.

BidDo Not Bid$12345678910$Win Contract

$\mathrm{.}8$Lose Contract

$\mathrm{.}2$Market ResearchNo Market ResearchForecast High

$\mathrm{.}6$Forecast Moderate

$\mathrm{.}4$Build ComplexSellBuild ComplexSellBuild ComplexSellHigh Demand

$\mathrm{.}85$High Demand

$\mathrm{.}225$High Demand

$\mathrm{.}6$Moderate Demand

$\mathrm{.}15$Moderate Demand

$\mathrm{.}775$Moderate Demand

$\mathrm{.}42,6506501,1502,6506501,1502,7807801,2802200$Profit $($$ $1,000$s$)$

An image of a decision tree is shown. Some of the branches eventually terminate at various values in a column labeled "Profit $($$ $1,000$s$)"$ on the right side of the image.

The decision tree begins at decision node $1$ and an upper and lower branch extend from this node to the right. The upper branch, labeled "Bid," stops at chance node $2$ and an upper and lower branch extend from this node to the right. The lower branch, labeled $"$Do Not Bid," extends all the way to the right and ends at a value of $0.$

The upper branch extending from chance node $2,$ labeled "Win Contract, $\mathrm{.}8,"$ stops at decision node $3$ and an upper and lower branch extend from this node to the right. The lower branch, labeled "Lose Contract, $\mathrm{.}2,"$ extends all the way to the right and ends at a value of $220.$

The upper branch extending from decision node $3,$ labeled "Market Research," stops at chance node $4$ and an upper and lower branch extend from this node to the right. The lower branch, labeled $"$No Market Research," stops at decision node $7$ and an upper and lower branch extend from this node to the right.

The upper branch extending from chance node $4,$ labeled "Forecast High, $\mathrm{.}6,"$ stops at decision node $5$ and an upper and lower branch extend from this node to the right. The lower branch, labeled "Forecast Moderate, $\mathrm{.}4,"$ stops at decision node $6$ and an upper and lower branch extend from this node to the right.

The upper branches extending from decision nodes $5,6,$ and $7,$ each labeled "Build Complex," stops at chance nodes $8,9,$ and $10,$ respectively, and an upper and lower branch extend from each of these nodes to the right. The lower branches extending from decision nodes $5,6,$ and $7,$ each labeled "Sell," extend all the way to the right and end at a values of $1,150,1,150,$ and $1,280,$ respectively.

The upper branch extending from chance node $8,$ labeled "High Demand, $\mathrm{.}85,"$ ends at a value of $2,650$ and the lower branch, labeled "Moderate Demand, $\mathrm{.}15,"$ ends at a value of $650.$ The upper branch extending from chance node $9,$ labeled "High Demand, $\mathrm{.}225,"$ ends at a value of $2,650$ and the lower branch, labeled "Moderate Demand, $\mathrm{.}775,"$ ends at a value of $650.$ The upper branch extending from chance node $10,$ labeled "High Demand, $\mathrm{.}6,"$ ends at a value of $2,780$ and the lower branch, labeled "Moderate Demand, $\mathrm{.}4,"$ ends at a value of $780.$

$($a$)$

Verify the company's profit projections shown at the ending branches of the decision tree by calculating the payoffs of $$2,650,000$ and $$650,000$ for first two outcomes, the outcomes extending from chance node $8.$

Outcome $1($$ in $1,000$s$)$

Bid

$5000$

Incorrect: Your answer is incorrect.

Contract

$2000$

Incorrect: Your answer is incorrect.

Market research

$130$

Incorrect: Your answer is incorrect.

High demand

$220$

Incorrect: Your answer is incorrect.

Total $$2,650$

Outcome $2($$ in $1,000$s$)$

Bid

$3000$

Incorrect: Your answer is incorrect.

Contract

$2000$

Incorrect: Your answer is incorrect.

Market research

$130$

Incorrect: Your answer is incorrect.

Moderate demand

$220$

Incorrect: Your answer is incorrect.

Total $$650$

$($b$)$

What is the optimal decision strategy for the company?

Bid on the contract. Do not do the market research. Build the complex.

Do not bid on the contract.

Bid on the contract. Do not do t