In a balanced transportation model, supply equals demand such that all constraints can betreated as equalities.
Fractional relationships between variables are permitted in the standard form of a linearprogram.
The standard form for the computer solution of a linear programming problem requires allvariables to be to the right and all numerical values to be to the left of the inequality or equalitysign
Product mix problems cannot have “greater than or equal to” (.) constraints.
In formulating a typical diet problem using a linear programming model, we would expect mostof the constraints to be related to calories.
In a transportation problem, a demand constraint (the amount of product demanded at a givendestination) is a less]than]or equal]to constraint (.).
Balanced transportation problems have the following type of constraints:
When systematically formulating a linear program, the first step is
A systematic approach to model formulation is to first
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 stipulatesthat stock 1 must not account for more than 35% of the number of shares purchased. Whichconstraint is correct?
The owner of Black Angus Ranch is trying to determine the correct mix of two types of beeffeed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essentialingredients are contained in the feed, shown in the table below. The table also shows theminimum daily requirements of each ingredient.IngredientPercent per poundin Feed APercent per poundin Feed BMinimum dailyrequirement(pounds)1 20 24 302 30 10 503 0 30 204 24 15 605 10 20 40The constraint for ingredient 3 is:
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 stockbroker suggests limiting the investments so that no more than$10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed350, whichever is more restrictive. How would this be formulated as a linear programmingconstraint?
The following types of constraints are ones that might be found in linear programmingformulations:1. .2. =3. >
The production manager for the Softy soft drink company is considering the production of 2kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce aregular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drinkare $2.00 per case. What is the time constraint?
Let xij = gallons of component i used in gasoline j. Assume that we have two components andtwo types of gasoline. There are 8,000 gallons of component 1 available, and the demandgasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraintfor component 1.
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%, and11%. An appropriate objective function is
Small motors for garden equipment is produced at 4 manufacturing facilities and needs to beshipped to 3 plants that produce different garden items (lawn mowers, rototillers, leafblowers). 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 manufacturingsite. The table below shows the cost to ship one unit between each manufacturing facility andeach plant, as well as the demand at each plant and the supply at each manufacturing facility.What is the demand constraint for plant B?
Compared to blending and product mix problems, transportation problems are unique because
Quickbrush Paint Company makes a profit of $2 per gallon on its oil]base paint and $3 pergallon on its water]base paint. Both paints contain two ingredients, A and B. The oil]base paintcontains 90 percent A and 10 percent B, whereas the water]base paint contains 30 percent Aand 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons ofingredient B in inventory and cannot obtain more at this time. The company wishes to uselinear programming to determine the appropriate mix of oil]base and water]base paint toproduce to maximize its total profit. How many gallons of water based paint should theQuickbrush make? Note: Please express your answer as a whole number, rounding the nearestwhole number, if appropriate.
Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the qualityof care the pets receive, including well balanced nutrition. The kennel’s cat food is made bymixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for thetwo cat foods are as follows:Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3ounces of fat per day. What is the cost of this plan? Express your answer with two places to theright of the decimal point. For instance, $9.32 (nine dollars and thirty]two cents) would bewritten as 9.32