### Coffee Blending ProblemDeluxe coffee is to be mixed with regular coffee to make at least 48 pounds of a blended coffee. The mixture must contain at least 9 pounds of deluxe coffee. Deluxe coffee costs $5 per pound and regular coffee $4 per pound. How many pounds of each kind of coffee should be used to minimize costs?---**Question:** To attain the minimum cost, use [ ] pounds of deluxe coffee and [ ] pounds of regular coffee.### ExplanationThis problem involves finding the optimal blend of two types of coffee to minimize costs while satisfying specified constraints. In mathematical terms, it's an optimization problem with constraints. 1. **Constraints:** - Total weight: at least 48 pounds - Minimum deluxe coffee: at least 9 pounds2. **Costs:** - Deluxe coffee: $5 per pound - Regular coffee: $4 per pound### Solution ApproachTo solve such a problem, we use linear programming techniques or a systematic approach to test possible combinations that satisfy the constraints.1. Let the amount of deluxe coffee be $ D $ pounds.2. Let the amount of regular coffee be $ R $ pounds.**Constraints:**- $ D + R \geq 48 $- $ D \geq 9 $**Objective:**Minimize cost, $ C $:\[ C = 5D + 4R \]By substituting potential values and ensuring all conditions are met, we can find the values of $ D $ and $ R $ that result in the minimum cost. The solution should be presented by filling the blanks in the question:**To attain the minimum cost, use [ ] pounds of deluxe coffee and [ ] pounds of regular coffee.** This transcription and explanation would help students understand the problem, constraints, and the approach to solve the optimization problem.

let x = Pounds of deluxe coffee let y = pounds of regular coffee x + y >= 48 The mix must have at…

Deluxe coffee is to be mixed with regular coffee to make at least pounds of a blended coffee. The mixture must contain at least 9 pounds of deluxe coffee. Deluxe coffee costs $5 per pound and regular coffee $4 per pound. How many pounds of each kind of coffee should be used to minimize costs? To attain the minimum cost, use pounds of deluxe coffee and pounds of regular coffee.

Deluxe coffee is to be mixed with regular coffee to make at least pounds of a blended coffee. The mixture must contain at least 9 pounds of deluxe coffee. Deluxe coffee costs $5 per pound and regular coffee $4 per pound. How many pounds of each kind of coffee should be used to minimize costs? To attain the minimum cost, use pounds of deluxe coffee and pounds of regular coffee.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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