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- Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?2. The figure below represents the traffic entering and leaving a roundabout road junction in Continental Europe. Such roundabouts ensure the continuous smooth flow of traffic at road junctions. Construct a system of linear equations describing the flow of traffic along the various branches. Use these equations to determine the minimum flow possible along xị. What are the other flows at this time? Explain what happens to x7 traffic. It is not necessary to compute the reduced echelon form. Use the fact the traffic flow can't be negative. The traffic is measured in vehicles per hour (vph). 90 A 100 X3 X2 X1 155 130 120 110 X6 X7 X5 80 75
- Explain what type of nodes do we choose to avoid the Runge phenomenon?The picture attached represents the traffic entering and leaving a "roundabout" road junction. Such junctions are very common in Europe. Construct a system of equations that describes the flow of traffic along the various branches. What is the minimum flow possible along the branch BC? What are the other flows at that time? (units are vehicles per hour.)At the BMV, suppose that the length of time you must wait before speaking to a customer service representative is linearly related to the number of people who are in line in front of you. If there are 8 people in line in front of you, you will wait 44 minutes, and if there are 14 people in front of you, you will wait 68 minutes. How long will you wait if there are 10 people in front of you?
- a. Find the general flow pattern of the network shown in the figure. 40 30 X2 b. Assuming that the flow must be in the directions indicated, find the minimum flows in the branches denoted by x2, x3, X5 Ic 100 (80 A X6 60 > E X3 X4 >80 X4, and x5. AD 20 50 a. Choose the correct answer below and fill in the answer boxes to complete your choice. O A. В. OC. OD. X, is free X1 = X1 = X1 = X2 = X2 is free X2 is free X2 = X3 X3 = X3 is free X3 is free X4 = X4 is free X4 is free X4 = X5 = X5 is free X5 is free X5 = X6 = X6 = X6 = X6 is freeSketch the graph of the system.Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following.
- Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following.Refer to Linear System and its graph of image shown belowEast Wind Community College had 6873 full-time male students enrolled in 2009 and 6567 full-time male students enrolled in 2006. Create a linear model for the enrollment of full-time male students at East Wind Community College. Let, represent years after 2000 E represent the enrollment of full-time male students E