MAT 540 Quiz Week 9 (SOLUTION 20/20)

Question Question 1 1. Fractional relationships between variables are permitted in the standard form of a linear program. Answer True False 2 points Question 2 1. In formulating a typical diet problem using a linear programming model we would expect most of the constraints to be related to calories. Answer True False 2 points Question 3 1. A constraint for a linear programming problem can never have a zero as its right-hand-side value. Answer True False 2 points Question 4 1. 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. Answer True False 2 points Question 5 1. Product mix problems cannot have “greater than or equal to” (?) constraints. Answer True False 2 points Question 6 1. When using a linear programming model to solve the “diet” problem the objective is generally to maximize profit. Answer True False 2 points Question 7 1. The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed A and B which cost 50 cents and 75 cents per pound respectively. Five essential ingredients are contained in the feed shown in the table below. The table also shows the minimum daily requirements of each ingredient. Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds) 1 20 24 30 2 30 10 50 3 0 30 20 4 24 15 60 5 10 20 40 The constraint for ingredient 3 is: Answer .5A + .75B = 20 .3B = 20 .3 B? 20 .3B ? 20 2 points Question 8 1. Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available and the demand gasoline types 1 and 2 are 11000 and 14000 gallons respectively. Write the supply constraint for component 1. Answer x21 + x22 ? 8000 x12 + x22 ? 8000 x11 + x12 ? 8000 x21 + x22 ? 8000 2 points Question 9 1. 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. Answer X21 + X22 + X23 ? 400 X21 + X22 + X23 ? 400 X12 + X22 + X32 ? 400 X12 + X22 + X32 ? 400 2 points Question 10 1. 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 production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients) 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 time constraint? Answer 2R + 4D ? 480 2D + 4R ? 480 2R + 3D ? 480 3R + 2D ? 480 2 points Question 11 1. 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: Answer .4×2 – .6×7 – .6×8 ? 0 x2 ? .60 (x2 + x7 + x8) .4×2 – .6×7 – .6×8 ? 0 -.4×2 + .6×7 + .6×8 ? 0 2 points Question 12 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 $50000 to invest. The stockbroker suggests limiting the investments so that no more than $10000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350 whichever is more restrictive. How would this be formulated as a linear programming constraint? Answer X2 ? 10000 X2 + X3 ?350 10000 X2 ? 350X2 + 350X3 47.25X2 ?10000 X2 + X3 ? 350 47.25X2 ?10000 47.25 X2 + 110X3 ? 350 2 points Question 13 1. A systematic approach to model formulation is to first Answer construct the objective function develop each constraint separately define decision variables all of the above 2 points Question 14 1. 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? Answer $220 $420 $320 $280 2 points Question 15 1. 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? Answer $380 $400 $420 $440 2 points Question 16 1. The following types of constraints are ones that might be found in linear programming formulations: 1. ? 2. = 3. > Answer 1 and 2 2 and 3 1 and 3 all of the above 2 points Question 17 1. 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? Answer x 1B + x 2B +x 3B = 600 x B1 + x B2 +x B3 = 150 x 1B + x 2B +x 3B = 150 none of the above 2 points Question 18 1. Compared to blending and product mix problems transportation problems are unique because Answer They maximize profit. The constraints are all equality constraints with no “?” or “?” constraints. They contain fewer variables. The solution values are always integers. 2 points Question 19 1. Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive including well balanced nutrition. The kennel’s cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the two cat foods are as follows: Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan?Express your answer with two places to the right of the decimal point.For instance $9.32(nine dollars and thirty-two cents) would be written as 9.32 2 points Question 20 1. 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 10000 gallons of ingredient A and 5000 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. Answer 2 points

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