Question Details

MAT 540
WEEK 9
 
When using a linear programming model to solve the "diet" problem, the objective is generally to maximize profit. 
 
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In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). 
 
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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. 
 
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The standard form for the computer solution of a linear programming problem requires all variables to be to the right and all numerical values to be to the left of the inequality or equality sign 
 
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A systematic approach to model formulation is to first construct the objective function before determining the decision variables. 
 
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A constraint for a linear programming problem can never have a zero as its right-hand-side value. 
 
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Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the 3 different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility. 
 
 
 
What is the demand constraint for plant B?
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If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company's 3 products in period 2 is equal to 400.
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A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit?
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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 2000 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 herbs. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $0.50.
What is the constraint for salt?
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In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively.  The investor has up to $50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and 11%.  An appropriate objective function is
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A systematic approach to model formulation is to first
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Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement can be written as:
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When systematically formulating a linear program, the first step is
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The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the optimal daily profit?
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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.
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In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased.  Which constraint is correct?
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The following types of constraints are ones that might be found in linear programming formulations:
1.
≤
2.
=
3.
> 
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Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How many gallons of oil based paint should the Quickbrush make? Note: Please express your answer as a whole number, rounding the nearest whole number, if appropriate.
 
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Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How many gallons of water based paint should the Quickbrush make? Note: Please express your answer as a whole number, rounding the nearest whole number, if appropriate.
 
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