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A pet food manufacturer produces two types of food: Regular and Premium. A 20kg bag of regular food requires 3 hours to prepare and 7/2 hours to cook. A 20kg bag of premium food requires 2 hours to prepare and 6 hours to cook. The materials used to prepare the food are available 7 hours per day, and the oven used to cook the food is available 17 hours per day. The profit on a 20kg bag of regular food is $30 and on a 20kg bag of premium food is $34. (a) What can the manager ask for directly? Profit in a day Preparation time in a day Number of bags of regular pet food made per day Oven time in a day Number of bags of premium pet food made per day The manager wants bags of regular food and y bags of premium pet food to be made in a day. (b) Enter the constraint imposed by available preparation time. It will be an inequality involving and y, you can enter less than or equal to, and greater than or equal to, as <= and >= respectively. (c) Enter the constraint imposed by available time in the oven. AG

A pet food manufacturer produces two types of food: Regular and Premium. A 20kg bag of regular food requires 3 hours to prepare and 7/2 hours to cook. A 20kg bag of premium food requires 2 hours to prepare and 6 hours to cook. The materials used to prepare the food are available 7 hours per day, and the oven used to cook the food is available 17 hours per day. The profit on a 20kg bag of regular food is $30 and on a 20kg bag of premium food is $34. (a) What can the manager ask for directly? Profit in a day Preparation time in a day Number of bags of regular pet food made per day Oven time in a day Number of bags of premium pet food made per day The manager wants bags of regular food and y bags of premium pet food to be made in a day. (b) Enter the constraint imposed by available preparation time. It will be an inequality involving and y, you can enter less than or equal to, and greater than or equal to, as <= and >= respectively. (c) Enter the constraint imposed by available time in the oven. AG

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CM: Cumulative Review Problem Set
Problem 115CM
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A pet food manufacturer produces two types of food: Regular and Premium. A 20kg bag of regular food requires 3 hours to prepare and 7/2 hours to cook. A 20kg bag of premium food requires 2 hours to prepare and 6 hours to cook. The materials used to prepare the food are available 7 hours per day, and the oven used to cook the food is available 17 hours per day. The profit on a 20kg bag of regular food is $30 and on a 20kg bag of premium food is $34. (a) What can the manager ask for directly? Profit in a day Preparation time in a day Number of bags of regular pet food made per day Oven time in a day Number of bags of premium pet food made per day The manager wants bags of regular food and y bags of premium pet food to be made in a day. (b) Enter the constraint imposed by available preparation time. It will be an inequality involving and y, you can enter less than or equal to, and greater than or equal to, as <= and >= respectively. (c) Enter the constraint imposed by available time in the oven. (d) Enter the total profit as a function of x and y. (e) Plot the inequalities on a graph. Enter the coordinates of the corners of the feasible region (the feasible basic solutions). Enter them in increasing order of their x-coordinate. For example, if one feasible basic solution is x = 1, y = 2; another is x = 5, y = 0 and a third is = 2, y = 3, you would enter (1,2), (2,3), (5,0) If two feasible basic solutions have the same x-value, enter them in increasing order of y-value. Enter them exactly, with fractions if necessary (they will just produce smaller bags) (f) Calculate the daily profit of each of these feasible basic solutions. What is the greatest possible profit in a day? Enter your answer exactly, or rounded to the nearest cent.
Transcribed Image Text:A pet food manufacturer produces two types of food: Regular and Premium. A 20kg bag of regular food requires 3 hours to prepare and 7/2 hours to cook. A 20kg bag of premium food requires 2 hours to prepare and 6 hours to cook. The materials used to prepare the food are available 7 hours per day, and the oven used to cook the food is available 17 hours per day. The profit on a 20kg bag of regular food is $30 and on a 20kg bag of premium food is $34. (a) What can the manager ask for directly? Profit in a day Preparation time in a day Number of bags of regular pet food made per day Oven time in a day Number of bags of premium pet food made per day The manager wants bags of regular food and y bags of premium pet food to be made in a day. (b) Enter the constraint imposed by available preparation time. It will be an inequality involving and y, you can enter less than or equal to, and greater than or equal to, as <= and >= respectively. (c) Enter the constraint imposed by available time in the oven. (d) Enter the total profit as a function of x and y. (e) Plot the inequalities on a graph. Enter the coordinates of the corners of the feasible region (the feasible basic solutions). Enter them in increasing order of their x-coordinate. For example, if one feasible basic solution is x = 1, y = 2; another is x = 5, y = 0 and a third is = 2, y = 3, you would enter (1,2), (2,3), (5,0) If two feasible basic solutions have the same x-value, enter them in increasing order of y-value. Enter them exactly, with fractions if necessary (they will just produce smaller bags) (f) Calculate the daily profit of each of these feasible basic solutions. What is the greatest possible profit in a day? Enter your answer exactly, or rounded to the nearest cent.
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