Solve the Problem Then a and B Represent the ʺCosts Per Dollar of Worth

question 59

Essay

Solve the problem.
-A company manufactures two products. For $1.00 worth of product A, the company
spends $0.40 on materials, $0.25 on labor, and $0.10 on overhead. For $1.00 worth of
product B, the company spends $0.50 on materials, $0.20 on labor, and $0.10 on overhead.
Let $$\mathbf { a } = \left[ \begin{array} { l } 0.40 \\0.25 \\0.10\end{array} \right] \text { and } \mathbf { b } = \left[ \begin{array} { l } 0.50 \\0.20 \\0.10\end{array} \right]$$ Then a and b represent the ʺcosts per dollar of incomeʺ for the two products.
Evaluate 100a + 400b and give an economic interpretation of the result.

Understand and apply the concept of direct and inverse proportionality in real-world scenarios.

Plot data points and interpret graphical representations of directly and inversely proportional relationships.

Calculate the constant of proportionality in direct and inverse proportionality equations.

Solve problems involving the relationship between variables in various formulas, including those of geometric figures like cylinders.

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Definitions:

Conservation

The practice of protecting the natural environment and preserving resources by managing and using them responsibly to prevent depletion.

Present Value

Today’s value of some amount of money that is to be received sometime in the future.

$50 Barrel

A pricing level for a barrel of crude oil, often used as a reference for energy market analysis and economic forecasting.

Extracting Oil

The process of removing crude oil from the earth through drilling or other methods to use as an energy source or in various industrial applications.