The following table shows observed electrical power consumption at several different levels of a factory's operation. Level 2 3 5 7 Power 1 3 3 5 Engineers want to fit the estimating relationship power = Bo + B1 · level to these data in a way that minimizes the sum of the absolute deviations between predicted and observed power requirements. Both parameters Bo and 31 should be nonnegative. Part I (10 points): Formulate an LP to choose optimal parameter values. Part II (5 points): Solve the LP using Matlab (linprog). Provide i) the optimal solution; ii) the optimal objective value; and iii) the matlab script used to solve the problem. Part III (10 + 5 points): Repeat the previous two steps, this time choosing a fit that minimizes the macimum deviation between observed and predicted power.