A contractor submits a bid on a project for which more...

A contractor submits a bid on a project for which more research and development work needs to be done. It is estimated that the total cost of satisfying the project specifications will be $$\$ 20$$ million plus the cost of the further research and development work. The contractor views the cost of this additional work as a random variable with a mean of $$\$ 4$$ million and a standard deviation of $$\$ 1$$ million. The contractor wishes to submit a bid such that his expected profit will be $10 \%$ of his expected costs. What should be the bid? If this bid is accepted, what will be the standard deviation of the profit made by the project?

Key Concepts

Profit Calculation and Markup Strategy

Profit calculation in project bidding involves determining the difference between the bid and the actual cost, where the bid is typically set by applying a certain margin to anticipated costs. A markup strategy is used to ensure that profit goals, expressed as a percentage of expected costs, are achieved, balancing competitive pricing with the necessary profit margin.

Linear Transformation of Random Variables

When a random variable is modified by a linear transformation—specifically scaling and shifting—the expected value and standard deviation are affected in predictable ways. Understanding these transformations is critical when determining the impact on profit or cost estimations that incorporate fixed costs and variable uncertainty.

Standard Deviation

Standard deviation is a measure of dispersion that indicates how much the values of a random variable typically deviate from the mean. In project cost analysis, the standard deviation helps quantify risk by showing the variability or uncertainty inherent in the random costs.

Expected Value

The expected value of a random variable represents the long?term average outcome over many trials. It is calculated by summing the products of possible outcomes and their probabilities. This concept is essential in cost estimation and decision making, where one uses the expected value to plan for average outcomes in the presence of uncertainty.

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