As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 400,000-400Q and P=900,000-2500, respectively. Your cost function is C(Q) = 125,000+ 430,0000. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes
As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 400,000-400Q and P=900,000-2500, respectively. Your cost function is C(Q) = 125,000+ 430,0000. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![**Title: Decision-Making in Residential Construction**
**Introduction:**
As the manager of Smith Construction, you face a critical decision regarding the number of homes to build in a new residential area where you are the sole builder. A significant challenge is that you must determine the volume of homes to construct without prior knowledge of the market demand. In this scenario, there's a 60 percent chance of encountering low demand and a 40 percent chance of high demand in this large neighborhood.
**Market Demand Scenarios:**
The (inverse) demand functions corresponding to these two scenarios are as follows:
1. **Low Demand Scenario:**
\[ P = 400,000 - 4000Q \]
2. **High Demand Scenario:**
\[ P = 900,000 - 2500Q \]
**Cost Function:**
Your cost function for the number of homes built is given by:
\[ C(Q) = 125,000 + 430,000Q \]
**Decision Point:**
How many new homes should you build, and what profits can you expect?
**Evaluation of Homes to Build:**
**Number of homes you should build:** ______ homes
Click here to understand how to calculate the optimal number of homes and expected profits based on the given demand and cost functions. Detailed explanations and step-by-step calculations are provided to guide you through the decision-making process.
**Conclusion:**
Making informed decisions in uncertain market conditions requires understanding demand scenarios and cost implications. As illustrated, a careful analysis can help in determining the optimal number of homes to build to maximize expected profits.
For more detailed information, visit our comprehensive guides on economic decision-making in construction management.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec969527-ef6f-4c91-8f92-7779f95f1ab5%2Fe8fb0c20-87bd-4c2e-a671-aff847d8456f%2Feeic49m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Decision-Making in Residential Construction**
**Introduction:**
As the manager of Smith Construction, you face a critical decision regarding the number of homes to build in a new residential area where you are the sole builder. A significant challenge is that you must determine the volume of homes to construct without prior knowledge of the market demand. In this scenario, there's a 60 percent chance of encountering low demand and a 40 percent chance of high demand in this large neighborhood.
**Market Demand Scenarios:**
The (inverse) demand functions corresponding to these two scenarios are as follows:
1. **Low Demand Scenario:**
\[ P = 400,000 - 4000Q \]
2. **High Demand Scenario:**
\[ P = 900,000 - 2500Q \]
**Cost Function:**
Your cost function for the number of homes built is given by:
\[ C(Q) = 125,000 + 430,000Q \]
**Decision Point:**
How many new homes should you build, and what profits can you expect?
**Evaluation of Homes to Build:**
**Number of homes you should build:** ______ homes
Click here to understand how to calculate the optimal number of homes and expected profits based on the given demand and cost functions. Detailed explanations and step-by-step calculations are provided to guide you through the decision-making process.
**Conclusion:**
Making informed decisions in uncertain market conditions requires understanding demand scenarios and cost implications. As illustrated, a careful analysis can help in determining the optimal number of homes to build to maximize expected profits.
For more detailed information, visit our comprehensive guides on economic decision-making in construction management.
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