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Chapter 9: Problem 5

A new energy company, All Green, has developed a new line of energy products. Top management is attempting to decide on both marketing and production strategies. Three strategies are considered and are referred to as \(A\) (aggressive), \(B\) (basic), and \(C\) (cautious). The conditions under which the study will be conducted are \(S\) (strong) and \(W\) (weak) conditions. Management's best estimates for net profits (in millions of dollars) are given in the following table. Build a decision tree to assist the company determine its best strategy. $$ \begin{array}{lcc} \hline \text { Decision } & \text { Strong (with probability } 45 \%) & \text { Weak (with probability 55\%) } \\ \hline A & 30 & -8 \\ B & 20 & 7 \\ C & 5 & 15 \\ \hline \end{array} $$

Short Answer

Expert verified
Strategy B with an expected profit of 12.65 million dollars.

Step by step solution

01

Understand the Problem

We need to determine which marketing and production strategy will yield the highest expected profit for All Green. The strategies are labeled as A, B, and C, and the market conditions can be strong (45% probability) or weak (55% probability). The objective is to calculate the expected profit for each strategy using these probabilities.
02

Calculate Expected Profits for Strategy A

The expected profit for strategy A can be calculated by multiplying each profit by its probability and adding the results. The formula is: \( E(A) = (0.45 \times 30) + (0.55 \times (-8)) \). Calculate this to get the expected profit for A.
03

Calculate Expected Profit for Strategy A

Using the formula from Step 2: \( E(A) = (0.45 \times 30) + (0.55 \times (-8)) = 13.5 - 4.4 = 9.1 \). The expected profit for strategy A is 9.1 million dollars.
04

Calculate Expected Profits for Strategy B

Similarly, calculate the expected profit for strategy B using the formula: \( E(B) = (0.45 \times 20) + (0.55 \times 7) \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Probability
When approaching decision-making problems, probability acts as a fundamental tool in predicting outcomes. In the context of All Green's decision analysis, we have two conditions: strong and weak, each with their own probabilities of occurrence. Probability is the mathematical representation of how likely an event is to occur, usually expressed as a number between 0 and 1. Here, the probability of a strong market condition is 0.45, meaning there is a 45% chance it will happen. Conversely, the probability of a weak market condition is 0.55, or 55% chance.

Probabilities must always sum to 1. This concept is crucial for creating a decision tree, as it allows us to weigh each potential outcome according to its likelihood. High probability means a higher chance of that market condition taking place, guiding decision-makers in allocating their resources effectively. By incorporating these probabilities into strategic calculations, companies like All Green gauge the potential risks and rewards of their decisions, thus formulating a more robust strategy.
Expected Profit
Expected profit is a crucial metric in decision tree analysis, particularly when companies are determining the potential gains or losses from different strategies. This concept combines both probabilities and potential profits to provide a single, anticipated value for each scenario. The formula for calculating expected profit involves multiplying the profit from each scenario by its probability, and then summing these products.

For Strategy A, for example, the expected profit was calculated as:
  • First, calculate for strong conditions: 0.45 probability x 30 million profit = 13.5 million
  • Next, for weak conditions: 0.55 probability x (-8) million profit = -4.4 million
Add the results: 13.5 million - 4.4 million = 9.1 million. Thus, the expected profit for strategy A stands at 9.1 million dollars. This measure helps in comparing different strategies as it encapsulates both risk (probability) and reward (profit) into a singular figure, guiding strategic decisions efficiently.
Decision Making
In business contexts such as All Green's energy product line strategy, decision making involves choosing among alternatives to achieve the highest benefit. Decision trees serve as valuable tools in this process by visually mapping out each choice, probability, and potential outcome. This method offers a clear understanding of complex scenarios through a structured and logical layout.

When engaging in decision making, management must weigh factors such as:
  • The expected profit of each strategy, which reflects both the probability of different market conditions and the associated gains or losses.
  • The probability of market conditions, which provides insight into the risk levels involved in each strategy.
  • Company goals and risk appetite, as some strategies may have higher potential but come with more significant risks.
By carefully evaluating these factors, decision-makers can choose the strategy that aligns best with the company鈥檚 objectives, optimizing for the best possible outcomes under given constraints.

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Most popular questions from this chapter

Given the following payoff matrix: $$ \begin{array}{llll} \hline & {\text { Conditions }} \\ \text { Alternative } & & & \\ \hline \text { A } & \$ 1000 & \$ 2000 & \$ 500 \\ \text { B } & \$ 800 & \$ 1200 & \$ 900 \\ \text { C } & \$ 700 & \$ 700 & \$ 700 \\ \hline \end{array} $$ Determine the best plan by each of the following criteria and show your work: a. Laplace b. Maximin c. \(\operatorname{Maximax}\) d. Coefficient of optimism (assume that \(x=0.55\) ) e. Regret (minimax)

For a new development area, a local investor is considering three alternative real estate investments: a hotel, a restaurant, and a convenience store. The hotel and the convenience store will be adversely or favorably affected depending on their closeness to the location of gasoline stations, which will be built in the near future. The restaurant will be assumed to be relatively stable. The payoffs for the investment are as follows: $$ \begin{array}{lccc} \hline & {\text { Conditions }} & \\ \text { Alternative } & \text { 1: Gas close } & \text { 2: Gas medium distance } & \text { 3: Gas far away } \\ \hline \text { Hotel } & \$ 25,000 & \$ 10,000 & -\$ 8000 \\ \text { Convenience store } & \$ 4000 & \$ 8000 & -\$ 12,000 \\ \text { Restaurant } & \$ 5000 & \$ 6000 & \$ 6000 \\ \hline \end{array} $$ Determine the best plan by each of the following criteria: a. Laplace b. Maximin c. Maximax d. Coefficient of optimism (assume that \(x=0.45\) ) e. Regret (minimax)

A big private oil company must decide whether to drill in the Gulf of Mexico. It costs \(\$ 1\) million to drill, and if oil is found its value is estimated at \(\$ 6\) million. At present, the oil company believes that there is a \(45 \%\) chance that oil is present. Before drilling begins, the big private oil company can hire a geologist for \(\$ 100,000\) to obtain samples and test for oil. There is only about a \(60 \%\) chance that the geologist will issue a favorable report. Given that the geologist does issue a favorable report, there is an \(85 \%\) chance that there is oil. Given an unfavorable report, there is a \(22 \%\) chance that there is oil. Determine what the big private oil company should do.

Consider a firm handling concessions for a sporting event. The firm's manager needs to know whether to stock up with coffee or cola and is formulating policies for specific weather predictions. A local agreement restricts the firm to selling only one type of beverage. The firm estimates a \(\$ 1500\) profit selling cola if the weather is cold and a \(\$ 5000\) profit selling cola if the weather is warm. The firm also estimates a \(\$ 4000\) profit selling coffee if it is cold and a \(\$ 1000\) profit selling coffee if the weather is warm. The weather forecast says that there is a \(30 \%\) of a cold front; otherwise, the weather will be warm. Build a decision tree to assist with the decision. What should the firm handling concessions do?

Assume the following probability distribution of daily demand for bushels of strawberries: $$ \begin{array}{lllll} \hline \text { Daily demand } & 0 & 1 & 2 & 3 \\ \text { Probability } & 0.2 & 0.3 & 0.3 & 0.2 \\ \hline \end{array} $$ Further assume that unit cost is \(\$ 3\) per bushel, selling price is \(\$ 5\) per bushel, and salvage value on unsold units is \(\$ 2\). We can stock \(0,1,2\), or 3 units. Assume that units from any single day cannot be sold on the next day. Build a decision tree and determine how many units should be stocked each day to maximize net profit over the long haul.
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