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High School Math Algebra High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

To State: The number of trays of each type of muffin that the baker should make to maximize profit. Maximum profit is earned when 3 trays of corn muffins and 2 trays of bran muffins are baked. Given: Baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flour. Baking a tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour. 16 cups of milk and 15 cups of wheat flour are available. A tray of corn muffins give a profit of $ 3 and that of bran muffins give a profit of $ 2 . Concepts Used: Modelling a situation as a Linear Programming Problem (LPP). Solving a LPP graphically. Calculations: Summarize the given information in a table: Corn Muffins Bran Muffins Total Number of Trays x y Cups of milk needed 4 x 2 y 4 x + 2 y Cups of wheat flour needed. 3 x 3 y 3 x + 3 y Profit 3 x 2 y 3 x + 2 y Write the constraints: 4 x + 2 y ≤ 16 is the constraint for the condition that there are 16 cups of milk available. 3 x + 3 y ≤ 15 are the constraints for the condition that there are 15 cups of wheat flour available. x ≥ 0 and y ≥ 0 are implicit constraints which impose the condition that the number of trays baked cannot be negative. 4 x + 2 y ≤ 16 3 x + 3 y ≤ 15 x ≥ 0 y ≥ 0 Write the objective function: the profit P = 3 x + 2 y to maximize. Determine the feasible region by graphing the constraint inequalities. Also determine the corner points of the feasible region. Evaluate the objective function P = 3 x + 2 y at the corner points. Corner Point x , y Value of Objective Function P = 3 x + 2 y 0 , 0 3 × 0 + 2 × 0 = 0 0 , 5 3 × 0 + 2 × 5 = 10 3 , 2 3 × 3 + 2 × 2 = 13 4 , 0 3 × 4 + 2 × 0 = 12 The maximum profit is $ 13 when 3 trays of corn muffins and 2 trays of bran muffins are baked. Conclusion: The maximum profit is $ 13 when 3 trays of corn muffins and 2 trays of bran muffins are baked.

To State: The number of trays of each type of muffin that the baker should make to maximize profit. Maximum profit is earned when 3 trays of corn muffins and 2 trays of bran muffins are baked. Given: Baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flour. Baking a tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour. 16 cups of milk and 15 cups of wheat flour are available. A tray of corn muffins give a profit of $ 3 and that of bran muffins give a profit of $ 2 . Concepts Used: Modelling a situation as a Linear Programming Problem (LPP). Solving a LPP graphically. Calculations: Summarize the given information in a table: Corn Muffins Bran Muffins Total Number of Trays x y Cups of milk needed 4 x 2 y 4 x + 2 y Cups of wheat flour needed. 3 x 3 y 3 x + 3 y Profit 3 x 2 y 3 x + 2 y Write the constraints: 4 x + 2 y ≤ 16 is the constraint for the condition that there are 16 cups of milk available. 3 x + 3 y ≤ 15 are the constraints for the condition that there are 15 cups of wheat flour available. x ≥ 0 and y ≥ 0 are implicit constraints which impose the condition that the number of trays baked cannot be negative. 4 x + 2 y ≤ 16 3 x + 3 y ≤ 15 x ≥ 0 y ≥ 0 Write the objective function: the profit P = 3 x + 2 y to maximize. Determine the feasible region by graphing the constraint inequalities. Also determine the corner points of the feasible region. Evaluate the objective function P = 3 x + 2 y at the corner points. Corner Point x , y Value of Objective Function P = 3 x + 2 y 0 , 0 3 × 0 + 2 × 0 = 0 0 , 5 3 × 0 + 2 × 5 = 10 3 , 2 3 × 3 + 2 × 2 = 13 4 , 0 3 × 4 + 2 × 0 = 12 The maximum profit is $ 13 when 3 trays of corn muffins and 2 trays of bran muffins are baked. Conclusion: The maximum profit is $ 13 when 3 trays of corn muffins and 2 trays of bran muffins are baked.

Solution Summary: The author states the number of trays of each type of muffin that the baker should make to maximize profit.

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

15th Edition

ISBN: 9780133281163

Author: Prentice Hall

Publisher: Prentice Hall

See similar textbooks

Expert Solution & Answer

Chapter 3.4, Problem 16PPSE

Solution

To State:

The number of trays of each type of muffin that the baker should make to maximize profit.

Maximum profit is earned when 3 trays of corn muffins and 2 trays of bran muffins are baked.

Given:

Baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flour.

Baking a tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour.

16 cups of milk and 15 cups of wheat flour are available.

A tray of corn muffins give a profit of $3 and that of bran muffins give a profit of $2 .

Concepts Used:

Modelling a situation as a Linear Programming Problem (LPP).

Solving a LPP graphically.

Calculations:

Summarize the given information in a table:

Corn Muffins Bran Muffins Total
Number of Trays x y
Cups of milk needed 4x 2y 4x+2y
Cups of wheat flour needed. 3x 3y 3x+3y
Profit 3x 2y 3x+2y

Write the constraints:

4x+2y≤16 is the constraint for the condition that there are 16 cups of milk available. 3x+3y≤15 are the constraints for the condition that there are 15 cups of wheat flour available. x≥0 and y≥0 are implicit constraints which impose the condition that the number of trays baked cannot be negative.

4x+2y≤163x+3y≤15x≥0y≥0

Write the objective function: the profit P=3x+2y to maximize.

Determine the feasible region by graphing the constraint inequalities. Also determine the corner points of the feasible region.

Evaluate the objective function P=3x+2y at the corner points.

Corner Point x,yValue of Objective Function P=3x+2y0,03×0+2×0=00,53×0+2×5=103,23×3+2×2=134,03×4+2×0=12

The maximum profit is $13 when 3 trays of corn muffins and 2 trays of bran muffins are baked.

Conclusion:

The maximum profit is $13 when 3 trays of corn muffins and 2 trays of bran muffins are baked.

Chapter 3.4, Problem 15PPSE

Chapter 3.4, Problem 17PPSE

Chapter 3 Solutions

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

Ch. 3.1 - Prob. 1LC Ch. 3.1 - Prob. 2LC Ch. 3.1 - Prob. 3LC Ch. 3.1 - Prob. 4LC Ch. 3.1 - Prob. 5LC Ch. 3.1 - Prob. 6LC Ch. 3.1 - Prob. 7PPSE Ch. 3.1 - Prob. 8PPSE Ch. 3.1 - Prob. 9PPSE Ch. 3.1 - Prob. 10PPSE

Ch. 3.1 - Prob. 11PPSE Ch. 3.1 - Prob. 12PPSE Ch. 3.1 - Prob. 13PPSE Ch. 3.1 - Prob. 14PPSE Ch. 3.1 - Prob. 15PPSE Ch. 3.1 - Prob. 16PPSE Ch. 3.1 - Prob. 17PPSE Ch. 3.1 - Prob. 18PPSE Ch. 3.1 - Prob. 19PPSE Ch. 3.1 - Prob. 20PPSE Ch. 3.1 - Prob. 21PPSE Ch. 3.1 - Prob. 22PPSE Ch. 3.1 - Prob. 23PPSE Ch. 3.1 - Prob. 24PPSE Ch. 3.1 - Prob. 25PPSE Ch. 3.1 - Prob. 26PPSE Ch. 3.1 - Prob. 27PPSE Ch. 3.1 - Prob. 28PPSE Ch. 3.1 - Prob. 29PPSE Ch. 3.1 - Prob. 30PPSE Ch. 3.1 - Prob. 31PPSE Ch. 3.1 - Prob. 32PPSE Ch. 3.1 - Prob. 33PPSE Ch. 3.1 - Prob. 34PPSE Ch. 3.1 - Prob. 35PPSE Ch. 3.1 - Prob. 36PPSE Ch. 3.1 - Prob. 37PPSE Ch. 3.1 - Prob. 38PPSE Ch. 3.1 - Prob. 39PPSE Ch. 3.1 - Prob. 40PPSE Ch. 3.1 - Prob. 41PPSE Ch. 3.1 - Prob. 42PPSE Ch. 3.1 - Prob. 43PPSE Ch. 3.1 - Prob. 44PPSE Ch. 3.1 - Prob. 45PPSE Ch. 3.1 - Prob. 46PPSE Ch. 3.1 - Prob. 47PPSE Ch. 3.1 - Prob. 48PPSE Ch. 3.1 - Prob. 49PPSE Ch. 3.1 - Prob. 50PPSE Ch. 3.1 - Prob. 51PPSE Ch. 3.1 - Prob. 52PPSE Ch. 3.1 - Prob. 53PPSE Ch. 3.1 - Prob. 54PPSE Ch. 3.1 - 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Prob. 35PPSE Ch. 3.4 - Prob. 36PPSE Ch. 3.4 - Prob. 37PPSE Ch. 3.4 - Prob. 1E Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.5 - Prob. 1A Ch. 3.5 - Prob. 2A Ch. 3.5 - Prob. 3A Ch. 3.5 - Prob. 4A Ch. 3.5 - Prob. 5A Ch. 3.5 - Prob. 6A Ch. 3.5 - Prob. 7A Ch. 3.5 - Prob. 8A Ch. 3.5 - Prob. 9A Ch. 3.5 - Prob. 10A Ch. 3.5 - Prob. 11A Ch. 3.5 - Prob. 12E Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Prob. 17E Ch. 3.5 - Prob. 18E Ch. 3.5 - Prob. 19E Ch. 3.5 - Prob. 20E Ch. 3.5 - Prob. 21E Ch. 3.5 - Prob. 22E Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 1LC Ch. 3.5 - Prob. 2LC Ch. 3.5 - Prob. 3LC Ch. 3.5 - Prob. 4LC Ch. 3.5 - Prob. 5LC Ch. 3.5 - Prob. 6LC Ch. 3.5 - Prob. 7LC Ch. 3.5 - Prob. 8LC Ch. 3.5 - Prob. 9PPSE Ch. 3.5 - Prob. 10PPSE Ch. 3.5 - Prob. 11PPSE Ch. 3.5 - Prob. 12PPSE Ch. 3.5 - Prob. 13PPSE Ch. 3.5 - Prob. 14PPSE Ch. 3.5 - Prob. 15PPSE Ch. 3.5 - Prob. 16PPSE Ch. 3.5 - Prob. 17PPSE Ch. 3.5 - Prob. 18PPSE Ch. 3.5 - Prob. 19PPSE Ch. 3.5 - Prob. 20PPSE Ch. 3.5 - Prob. 21PPSE Ch. 3.5 - Prob. 22PPSE Ch. 3.5 - Prob. 23PPSE Ch. 3.5 - Prob. 24PPSE Ch. 3.5 - Prob. 25PPSE Ch. 3.5 - Prob. 26PPSE Ch. 3.5 - Prob. 27PPSE Ch. 3.5 - Prob. 28PPSE Ch. 3.5 - Prob. 29PPSE Ch. 3.5 - Prob. 30PPSE Ch. 3.5 - Prob. 31PPSE Ch. 3.5 - Prob. 32PPSE Ch. 3.5 - Prob. 33PPSE Ch. 3.5 - Prob. 34PPSE Ch. 3.5 - Prob. 35PPSE Ch. 3.5 - Prob. 36PPSE Ch. 3.5 - Prob. 37PPSE Ch. 3.5 - Prob. 38PPSE Ch. 3.5 - Prob. 39PPSE Ch. 3.5 - Prob. 40PPSE Ch. 3.5 - Prob. 41PPSE Ch. 3.5 - Prob. 42PPSE Ch. 3.5 - Prob. 43PPSE Ch. 3.5 - Prob. 44PPSE Ch. 3.5 - Prob. 45PPSE Ch. 3.6 - Prob. 1LC Ch. 3.6 - Prob. 2LC Ch. 3.6 - Prob. 3LC Ch. 3.6 - Prob. 4LC Ch. 3.6 - Prob. 5LC Ch. 3.6 - Prob. 6LC Ch. 3.6 - Prob. 7LC Ch. 3.6 - Prob. 8PPSE Ch. 3.6 - Prob. 9PPSE Ch. 3.6 - Prob. 10PPSE Ch. 3.6 - Prob. 11PPSE Ch. 3.6 - Prob. 12PPSE Ch. 3.6 - Prob. 13PPSE Ch. 3.6 - Prob. 14PPSE Ch. 3.6 - Prob. 15PPSE Ch. 3.6 - Prob. 16PPSE Ch. 3.6 - Prob. 17PPSE Ch. 3.6 - Prob. 18PPSE Ch. 3.6 - Prob. 19PPSE Ch. 3.6 - Prob. 20PPSE Ch. 3.6 - Prob. 21PPSE Ch. 3.6 - Prob. 22PPSE Ch. 3.6 - Prob. 23PPSE Ch. 3.6 - Prob. 24PPSE Ch. 3.6 - Prob. 25PPSE Ch. 3.6 - Prob. 26PPSE Ch. 3.6 - Prob. 27PPSE Ch. 3.6 - Prob. 28PPSE Ch. 3.6 - Prob. 29PPSE Ch. 3.6 - Prob. 30PPSE Ch. 3.6 - Prob. 31PPSE Ch. 3.6 - Prob. 32PPSE Ch. 3.6 - Prob. 33PPSE Ch. 3.6 - Prob. 34PPSE Ch. 3.6 - Prob. 35PPSE Ch. 3.6 - Prob. 36PPSE Ch. 3.6 - Prob. 37PPSE Ch. 3.6 - Prob. 38PPSE Ch. 3.6 - Prob. 39PPSE Ch. 3.6 - Prob. 40PPSE Ch. 3.6 - Prob. 41PPSE Ch. 3.6 - Prob. 42PPSE Ch. 3.6 - Prob. 43PPSE Ch. 3.6 - Prob. 44PPSE Ch. 3.6 - Prob. 45PPSE Ch. 3.6 - Prob. 46PPSE Ch. 3.6 - Prob. 47PPSE Ch. 3.6 - Prob. 48PPSE Ch. 3.6 - Prob. 49PPSE Ch. 3.6 - Prob. 50PPSE Ch. 3.6 - Prob. 51PPSE Ch. 3.6 - Prob. 52PPSE Ch. 3.6 - Prob. 53PPSE Ch. 3.6 - Prob. 54PPSE Ch. 3.6 - Prob. 55PPSE Ch. 3.6 - Prob. 56PPSE Ch. 3.6 - Prob. 57PPSE Ch. 3.6 - Prob. 58PPSE Ch. 3 - Prob. 1GR Ch. 3 - Prob. 2GR Ch. 3 - Prob. 3GR Ch. 3 - Prob. 4GR Ch. 3 - Prob. 5GR Ch. 3 - Prob. 6GR Ch. 3 - Prob. 7GR Ch. 3 - Prob. 8GR Ch. 3 - Prob. 9GR Ch. 3 - Prob. 10GR Ch. 3 - Prob. 11GR Ch. 3 - Prob. 12GR Ch. 3 - Prob. 13GR Ch. 3 - Prob. 14GR Ch. 3 - Prob. 15GR Ch. 3 - Prob. 16GR Ch. 3 - Prob. 17GR Ch. 3 - Prob. 18GR Ch. 3 - Prob. 19GR Ch. 3 - Prob. 20GR Ch. 3 - Prob. 21GR Ch. 3 - Prob. 22GR Ch. 3 - Prob. 23GR Ch. 3 - Prob. 1MCQ Ch. 3 - Prob. 2MCQ Ch. 3 - Prob. 3MCQ Ch. 3 - Prob. 4MCQ Ch. 3 - Prob. 5MCQ Ch. 3 - Prob. 6MCQ Ch. 3 - Prob. 7MCQ Ch. 3 - Prob. 8MCQ Ch. 3 - Prob. 9MCQ Ch. 3 - Prob. 10MCQ Ch. 3 - Prob. 11MCQ Ch. 3 - Prob. 12MCQ Ch. 3 - Prob. 13MCQ Ch. 3 - Prob. 14MCQ Ch. 3 - Prob. 15MCQ Ch. 3 - Prob. 16MCQ Ch. 3 - Prob. 17MCQ Ch. 3 - Prob. 18MCQ Ch. 3 - Prob. 1CV Ch. 3 - Prob. 2CV Ch. 3 - Prob. 3E Ch. 3 - Prob. 4E Ch. 3 - Prob. 5E Ch. 3 - Prob. 6E Ch. 3 - Prob. 7E Ch. 3 - Prob. 8E Ch. 3 - Prob. 9E Ch. 3 - Prob. 10E Ch. 3 - Prob. 11E Ch. 3 - Prob. 12E Ch. 3 - Prob. 13E Ch. 3 - Prob. 14E Ch. 3 - Prob. 15E Ch. 3 - Prob. 16E Ch. 3 - Prob. 17E Ch. 3 - Prob. 18E Ch. 3 - Prob. 19E Ch. 3 - 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