1 Find the differential equations representing the system shown in the Figure. ly

Suppose you want to solve the following LP: maxcTx: Ax≤b, but unfortunately it is infeasible (think e.g. about an inventory problem where the demand cannot be satisfied by the warehouse). Let A ∈ Rm×n. Now suppose you can “augment” your LP by buying some more slack in your problem (think e.g. of buying some of the product from other warehouses). In particular, for i = 1, . . . , m, if you want to increase the right-hand side of the i-th constraint by some value λi, you will pay diλi for some fixed number di. Suppose moreover that the right-hand side of the i-th constraint can be augmented by at most ki, for i = 1,...,m. How can you find the optimal augmentation, i.e. the one that maximizes the profit of the optimal solution of the augmented LP minus the cost for the augmentation?

d) Initially, the string is at rest at the profile {y2  y3  y4}0 = {0.4  0.7  0.3}. Use the answer in part c) to find {y2  y3  y4}1. Show all the necessary calculations.  e) Thus, further calculations to show one cycle (periodical process) are obtained by tabulating a table.   f) Based on the problem statement given in part e), use MS Excel to plot a graph of displacement y against x.

The Johnson & Royce model of a distillation column is driven by the inputs of steam flow and its flow rate; the output measurement is the temperature change. The state-space model is given by: -2 x = [¯²¯¯¯7 | x + | | | u; y = [0_1]x - the system defining the model of the distillation column is a. Asymptotically stable O b. Unstable Oc. Marginally stable Od. Indeterminate in relation to its stability