Consider the network below with the following link travel time functions Xa is the flow (users) on link a; ta is the travel time of link a in minutes t₁(x1) = x₁ + 3 t₂(x2) = 2x2 + 1 t3(x3) = 3x3 t4(x4) = 22 t5(x5)= X5 1 2 X2 = C1D + c2 c1= c2= 5 3 3 4 Let D be the demand for the O-D pair (1, 4). (b) Assuming all paths are used at User-Equilibrium, express the link flow X2 as a function of D (Provide the values in 3 decimal places).

Suppose that the number of tee shirts sold (N) depends linearly on the price charged (x). Write an equation showing this dependence.

Determine whether 2 4 are linearly independent.

Define Linearly Dependence and give on example

The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below.    Price 0.00 0.45 0.60 0.75 1.00 1.25 1.40 1.50 Profit 0.00 $720 $900 $990 $845 $625 $560 $300     What factors might influence how much is to be made from the candy sale? Give at least  two.             What happens to the profit as the price of each candy bar increases?  Explain possible reasons for your observations.               How do you suppose the other bands determined the price at which to sell each candy bar?         Do any data values seem unusual? Yes or…