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Question 1
Let d represent the number of donuts Hermione bakes, and let c represent the number of croissants Hermione bakes. Select all the linear inequalities that should be included to model the total number of pastries Hermione should sell to maximize her profits.
Answer: Correct! Go to question 2.
Answer: Incorrect. The answers are:
B. d ≥ 20d is greater than or equal to 20
D. c ≥ 20c is greater than or equal to 20
E. d + c ≤ 90d plus c is less than or equal to 90
G. 0.75d + 1.35c ≤ 100seventy five hundredths d plus one and thirty five hundredths c is less than or equal to 100
From the scenario given: “Hermione decides to expand her bakery business to include donuts and croissants. She makes no more than a total of 90 of these pastries (d + c ≤ 90c is less than or equal to 90), but bakes at least 20 of each (d ≥ 20 and c ≥ 20d is greater than or equal to 20 and c is greater than or equal to 20), every day. Because these two pastries are new to Hermione’s business, she wants to keep track of the costs to produce them. Each donut costs $0.75 to produce, while each croissant costs $1.35 to produce. Until she sees how well these pastries sell, she does not want production costs to exceed $100 (0.75d + 1.35c ≤ 100seventy five hundredths d plus one and thirty five hundredths c is less than or equal to 100).
Go to question 2.
B. d ≥ 20d is greater than or equal to 20
D. c ≥ 20c is greater than or equal to 20
E. d + c ≤ 90d plus c is less than or equal to 90
G. 0.75d + 1.35c ≤ 100seventy five hundredths d plus one and thirty five hundredths c is less than or equal to 100
From the scenario given: “Hermione decides to expand her bakery business to include donuts and croissants. She makes no more than a total of 90 of these pastries (d + c ≤ 90c is less than or equal to 90), but bakes at least 20 of each (d ≥ 20 and c ≥ 20d is greater than or equal to 20 and c is greater than or equal to 20), every day. Because these two pastries are new to Hermione’s business, she wants to keep track of the costs to produce them. Each donut costs $0.75 to produce, while each croissant costs $1.35 to produce. Until she sees how well these pastries sell, she does not want production costs to exceed $100 (0.75d + 1.35c ≤ 100seventy five hundredths d plus one and thirty five hundredths c is less than or equal to 100).
Go to question 2.
Answer: Incorrect. Review the Learn It section, and then try again.
Select an answer from the options below and click Submit.
Question 2
Use your graphing calculator to graph the system of linear equations:
Which graph below is correct?
Answer: Correct! Go to question 3.
Answer: Incorrect. The answer is B. Go to question 3.
A coordinate grid with the x axis labeled Number of Donuts Baked and the variable d, extending from 0 to 150 in increments of 10, and the y axis labeled Number of Croissants Baked and the variable c, extending from 0 to 100 in increments of 10. Four inequalities are graphed. A solid vertical line is graphed at d equals 20 and the shading is to the right of the line. A solid horizontal line is graphed at c equals 20 and the shading is above the line. A solid line is graphed with a y intercept of 90 and has a slope of negative 1. The shading is below the line. A solid line is graphed with a y intercept of approximately seventy four and seven hundredths and a slope of five ninths. The shading is below the line.
A coordinate grid with the x axis labeled Number of Donuts Baked and the variable d, extending from 0 to 150 in increments of 10, and the y axis labeled Number of Croissants Baked and the variable c, extending from 0 to 100 in increments of 10. Four inequalities are graphed. A solid vertical line is graphed at d equals 20 and the shading is to the right of the line. A solid horizontal line is graphed at c equals 20 and the shading is above the line. A solid line is graphed with a y intercept of 90 and has a slope of negative 1. The shading is below the line. A solid line is graphed with a y intercept of approximately seventy four and seven hundredths and a slope of five ninths. The shading is below the line.
Answer:Incorrect. Review the Learn It section, and then try again.
Select an answer(s) from the options below and click Submit.
Question 3
Identify the vertices of the common shaded region formed by the system of linear inequalities.
Answer: Correct! Go to question 4.
Answer: Incorrect. The answers are:
B. (20, 20)
C. (70, 20)
E. (20, 62.96)
G. (35.83, 54.17)
A coordinate grid with the x axis labeled Number of Donuts Baked and the variable d, extending from 0 to 150 in increments of 10, and the y axis labeled Number of Croissants Baked and the variable c, extending from 0 to 100 in increments of 10. Four inequalities are graphed. A solid vertical line is graphed at d equals 20 and the shading is to the right of the line. A solid horizontal line is graphed at c equals 20 and the shading is above the line. A solid line is graphed with a y intercept of 90 and has a slope of negative 1. The shading is below the line. A solid line is graphed with a y intercept of approximately seventy four and seven hundredths and a slope of five ninths. The shading is below the line. Four points are plotted at the intersections of the four solid lines: (20, 20), (70, 20), (20, 62.96) and (35.83, 54.17).
To find the intersection points of each linear pair, use the calculation feature of your graphing calculator. For example, to find the intersection of d + c ≤ 90d plus c is less than or equal to 90 and 0.75d + 1.35c ≤ 100seventy five hundredths d plus one and thirty five hundredths c is less than or equal to 100:
A calculator screen shot showing y sub 1 equals 90 minus x and y sub 2 equals 100 divided by one and thirty five hundredths minus seventy five hundredths x divided by one and thirty five hundredths
A calculator screen shot showing the graph of the two lines entered
A calculator screen shot displaying the Calculate menu with option 5 intersect chosen
A calculator screen shot showing the lines graphed and the intersection of the lines at x equals approximately thirty five and eighty three hundredths and y equals approximately fifty four and seventeen hundredths
Go to question 4.
B. (20, 20)
C. (70, 20)
E. (20, 62.96)
G. (35.83, 54.17)
A coordinate grid with the x axis labeled Number of Donuts Baked and the variable d, extending from 0 to 150 in increments of 10, and the y axis labeled Number of Croissants Baked and the variable c, extending from 0 to 100 in increments of 10. Four inequalities are graphed. A solid vertical line is graphed at d equals 20 and the shading is to the right of the line. A solid horizontal line is graphed at c equals 20 and the shading is above the line. A solid line is graphed with a y intercept of 90 and has a slope of negative 1. The shading is below the line. A solid line is graphed with a y intercept of approximately seventy four and seven hundredths and a slope of five ninths. The shading is below the line. Four points are plotted at the intersections of the four solid lines: (20, 20), (70, 20), (20, 62.96) and (35.83, 54.17).To find the intersection points of each linear pair, use the calculation feature of your graphing calculator. For example, to find the intersection of d + c ≤ 90d plus c is less than or equal to 90 and 0.75d + 1.35c ≤ 100seventy five hundredths d plus one and thirty five hundredths c is less than or equal to 100:
A calculator screen shot showing y sub 1 equals 90 minus x and y sub 2 equals 100 divided by one and thirty five hundredths minus seventy five hundredths x divided by one and thirty five hundredths
A calculator screen shot showing the graph of the two lines entered
A calculator screen shot displaying the Calculate menu with option 5 intersect chosen
A calculator screen shot showing the lines graphed and the intersection of the lines at x equals approximately thirty five and eighty three hundredths and y equals approximately fifty four and seventeen hundredths
Go to question 4.
Answer: Incorrect. Try again. Use the calculation features of your graphing calculator to find the exact intersection points.
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Question 4
Hermione makes $0.25 from each donut and $0.75 from each croissant she sells. Which objective function represents the total profit she makes from selling these pastries?
Answer: Correct!
Answer: Incorrect. The answer is A.
According to the scenario: “Hermione makes $0.25 from each donut (0.25dtwenty five hundredths d) and $0.75 from each croissant (0.75cseventy five hundredths c) she sells.”
According to the scenario: “Hermione makes $0.25 from each donut (0.25dtwenty five hundredths d) and $0.75 from each croissant (0.75cseventy five hundredths c) she sells.”
Answer:Incorrect. Review the Learn It section, and then try again.