Determine the Values of X and Y That Produce the Minimum

question 31

Multiple Choice

Determine the values of x and y that produce the minimum value of the objective function on the feasible
region. Determine the minimum value of the objective function on the feasible region.
- $$\begin{array} { l } x \geq 0 , y \geq 0 \\40 x + 30 y \geq 3,200 \\x \geq 1.75 y \\\quad \text { Minimize } z = 22 x + 12 y\end{array}$$

• A) \(x = 32 , y = 56\); Minimum value: 48,320
• B) \(x = 32 , y = 56\); Minimum value: 1,376
• C) \(x = 56 , y = 32\); Minimum value: 60,800
• D) \(x = 56 , y = 32\); Minimum value: 1,616

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Definitions:

Goodness of Fit

A statistical measure that indicates how well observed data correspond to the expected outcome under a specified model.

Direct Cost

Expenses that can be directly traced to the production of specific goods or services, such as raw materials and labor.

Hourly Labour

Refers to workers who are paid for each hour of work they perform, as opposed to salaried employees who receive a fixed amount regardless of hours worked.

Kitchen Benchtops

The flat surfaces in a kitchen on which food can be prepared, often made from materials such as stone, laminate, or timber.