Linear Programming : Defining Costraints and Maximizing Profit
Not what you're looking for?
Tom and Jerry, Inc., supplies its ice cream parlors with three flavors of ice cream: chocolate, vanilla, and banana. Due to extremely hot weather and a high demand for its products, the company has run short of its supply of ingredients: milk, sugar, and cream. Hence, they will not be able to fill all the orders received from their retail outlets, the ice cream parlors. Due to these circumstances, the company has decided to choose the amount of each flavor to produce that will maximize total profit, given the constraints on supply of the basic ingredients.
The chocolate, vanilla, and banana flavors generate, respectively, $1.00, $0.90, and $0.95 of profit per gallon sold. The company has only 200 gallons of milk, 150 pounds of sugar, and 60 gallons of cream left in its inventory. The linear programming formulation for this problem is shown below in algebraic form.
Let C = gallons of chocolate ice cream produced,
V = gallons of vanilla ice cream produced,
B = gallons of banana ice cream produced.
Maximize Profit = 1.00 C + 0.90 V + 0.95 B,
subject to
Milk: 0.45 C + 0.50 V + 0.40 B ≤ 200 gallons
Sugar: 0.50 C + 0.40 V + 0.40 B ≤ 150 pounds
Cream: 0.10 C + 0.15 V + 0.20 B ≤ 60 gallons
and
C ≥ 0, V ≥ 0, B ≥ 0.
This problem was solved using the Excel Solver. The spreadsheet (already solved) and the sensitivity report are shown below. [Note: The numbers in the sensitivity report for the milk constraint are missing on purpose, since you will be asked to fill in these numbers in part (f).]
See attached file for full problem description.
Purchase this Solution
Solution Summary
An LP problem is solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
Solution Preview
Please see attached file.
Tom and Jerry, Inc., supplies its ice cream parlors with three flavors of ice cream: chocolate, vanilla, and banana. Due to extremely hot weather and a high demand for its products, the company has run short of its supply of ingredients: milk, sugar, and cream. Hence, they will not be able to fill all the orders received from their retail outlets, the ice cream parlors. Due to these circumstances, the company has decided to choose the amount of each flavor to produce that will maximize total profit, given the constraints on supply of the basic ingredients.
The chocolate, vanilla, and banana flavors generate, respectively, $1.00, $0.90, and $0.95 of profit per gallon sold. The company has only 200 gallons of milk, 150 pounds of sugar, and 60 gallons of cream left in its inventory. The linear programming formulation for this problem is shown below in algebraic form.
Let C = gallons of chocolate ice cream produced,
V = gallons of vanilla ice cream produced,
B = gallons of banana ice cream produced.
Maximize Profit = 1.00 C + 0.90 V + 0.95 B,
subject to
Milk: 0.45 C + 0.50 V + 0.40 B ≤ 200 gallons
Sugar: 0.50 C + 0.40 V + 0.40 B ≤ 150 pounds
Cream: 0.10 C + 0.15 V + 0.20 B ≤ 60 ...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability