Find the Maximum Value of the Objective Function and Where $z = 6 x - 7 y$

question 47

Multiple Choice

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. (You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values.) Objective function: $z = 6 x - 7 y$ Constraints: $$\left\{ \begin{array} { l } x \geq 0 \\y \geq 0 \\5 x + 4 y \leq 20 \\3 x + 2 y \leq 6\end{array} \right.$$

• A) \(\text { maximum } = 24 \text { at } ( 4,0 )\)
• B) \(\text { maximum } = 12 \text { at } ( 2,0 )\)
• C) \(\text { maximum } = 35 \text { at } ( 0,5 )\)
• D) \(\text { The maximum is unbounded. }\)
• E) \(\text { There is no maximum. The feasable solution set is empty. }\)

---

Definitions:

Cure and Smoke

The process of preserving and flavoring food, particularly meats, by applying a combination of salt, nitrates, and sometimes sugar (curing) and then exposing it to smoke from burning or smoldering material, usually wood (smoking).

Revocation Effective

The point in time when the cancellation or withdrawal of a legal privilege, right, or contract becomes officially valid.

Irrevocable Offer

An offer that cannot be withdrawn or revoked for a certain period once made, holding the offeror to their promise.

Roasting Services

A business service centered on processing coffee beans or other products by applying heat to achieve desired flavors.