Use Inequalities to Describe Limitations in a Situation
-A Steel $\$ 0.75$

question 273

Multiple Choice

Use Inequalities to Describe Limitations in a Situation
-A steel company produces two types of machine dies, part A and part B and is bound by the following constraints:
- Part A requires 1 hour of casting time and 10 hours of firing time.
- Part B requires 4 hours of casting time and 3 hours of firing time.
- The maximum number of hours per week available for casting and firing are 100 and 70 , respectively.
- The cost to the company is $\$ 0.75$ per part $A$ and $\$ 3.00$ per part $B$ . Total weekly costs cannot exceed $\$ 45.00$ .
Let $\mathrm { x } =$ the number of part A produced in a week and $\mathrm { y } =$ the number of part B produced in a week. Write a system of three inequalities that describes these constraints.

• A)
• \(\begin{array}{r}
• x+4 y \leq 100 \\
• 10 x+3 y \leq 70 \\
• 0.75 x+3 y \leq 45
• \end{array}\)
• B)\(\begin{array}{r}
• x+10 y \leq 100 \\
• 4 x+3 y \leq 70 \\
• 0.75 x+3 y \leq 45
• \end{array}\)
• C)\(\begin{array}{r}
• x+10 y \geq 100 \\
• 4 x+3 y \geq 70 \\
• 0.75 x+3 y \leq 45
• \end{array}\)
• D)
• \[\begin{array} { r r }
• x + & 4 y \leq 100 \\
• 10 x + 3 y \leq & 70 \\
• 3 x + 0.75 y \leq & 45
• \end{array}\]

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Definitions:

Regression Analysis

Regression Analysis is a statistical method used to investigate and model the relationship between variables, typically one dependent variable and one or more independent variables.

Constant Variance

The condition in which the variance of error terms in a regression model is the same across all levels of the independent variables.

Error Variable

A variable in statistical or mathematical models that represents the difference between observed and predicted values, often due to randomness or unexplained variation.

Outliers

Outliers are data points that deviate significantly from the rest of the data, potentially indicating variability in the measurement or experimental errors.