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# Determine the production quantities through linear programming

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(See attached file for full problem description)

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Indicate whether the sentence or statement is true or false.

_____ 1. Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem.

_____ 2. When using linear programming model to solve the "diet" problem, the objective is generally to maximize profit.

_____ 3. The standard form for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign.

_____ 4. In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure.

_____ 5. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

Identify the letter of the choice that best completes the statement or answers the question.

_____ 6. Which solutions are ones that satisfy all the constraints simultaneously?
a. alternate
b. feasible
c. infeasible
d. optimal

_____ 7. The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 200 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of salt. Profits for a bag of Lime chips are \$0.40, and for a bag of Vinegar chips \$0.50. What is the objective function?

a. Z = \$0.50L + \$0.40V
b. Z = \$0.40L + \$0.50V
c. Z = \$0.20L + \$0.30V
d. Z = \$0.30L + \$0.20V

_____ 8. Profit is maximized in the objective function by
a. subtracting cost from revenue
b. subtracting revenue from cost
d. multiplying revenue by cost

_____ 9. Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.
a. x21 + x22 <= 8000
b. x12 + x22 >= 8000
c. X11 + x12 <= 8000
d. X12 + x22 <= 8000

_____ 10. A systematic approach to model formulation is to first
a. construct the objective function
b. develop each constraint separately
c. define decision variables
d. determine the right hand side of each constraint

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(See attached file for full problem description)

##### Solution Summary

This helps to determine the truth of several statements regarding linear programming and also briefly shows how to set up linear programming problems.

Solution provided by:
###### 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!"
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