Use Mathematical Models Involving Linear Inequalities
-A Bakery Plans to Market

question 55

Multiple Choice

Use Mathematical Models Involving Linear Inequalities
-A bakery plans to market a mixed assortment of its two most popular cookies, Chocolate Chip and Toffee Chunk. The marketing analyst proposes that the new assortment be constrained by the inequality 3C + 4T ≤ 31, where C is the number of Chocolate Chip cookies and T is the number of Toffee Chunk cookies. The sales analyst suggests that the assortment should be constrained by the inequality 5C + 2T ≤ 33. The number of each type of cookie cannot be negative, so C ≥ 0 and T ≥ 0. Graph the region satisfying all the requirements for the assortment using C as the horizontal axis and T as the vertical axis. Does the combination of 7 Chocolate Chip cookies and 2 Toffee Chunk cookies satisfy all of the requirements?

• A) \(\mathrm { No }\)
• B) Yes
• C) No
• D) Yes

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Definitions:

Production Possibility Frontier

A graph showing all the highest production outcomes for two or more products based on a certain amount of inputs (like resources and labor), illustrating the compromises in the production levels among various goods.

Resources Improvements

Enhancements or upgrades to the inputs used in the production process, including technology, labor skills, and machinery, leading to increased efficiency or productivity.

Technology Increase

Refers to advancements or improvements in technology that enhance productivity or efficiency.

Comparative Advantage

The capability of an entity, whether it be a person, company, or nation, to create a good or offer a service more efficiently, in terms of opportunity cost, than competitors.