A rental car company has an imbalance of cars at seven of its locations. The following net- work shows the locations of concern (the nodes) and the cost to move a car between loca- tions. A positive number by a node indicates an excess supply at the node, and a negative number indicates an excess demand.

Suppose you believe that population abundance (A) of a particular species is a linear function of vegetation coverage (V) and the presence of a predators (P). Surveys where conducted across 20 sites and found the following information: a) There was an average of cover of .406 (40.6%) of the area, with an average 6.8 predators and 61.55 individuals in our target population. b) ⟨V2⟩=0.231⟨V2⟩=0.231, ⟨P2⟩=76.300⟨P2⟩=76.300, ⟨VP⟩=2.933⟨VP⟩=2.933, ⟨VA⟩=36.329⟨VA⟩=36.329, ⟨PA⟩=379.300⟨PA⟩=379.300 Set up the appropriate system of equations needed for a the linear regression of a model of the form A=aV+bP+cA=aV+bP+c. Then estimate the parameters and report the final model.

ii) A contractor owns three excavators of different capacity. He/she wants to dispatch these excavators into three different jobs. The performance of the excavators is measured as the time consumed to perform each job. The data of the time tests are shown as given in the table below. Job time (hour) Job 1 Job 2 Job 3 Excavator 1 5 4 9. 4 10 8 3 10 3 (a) Draw a network flow diagram. (b) Formulate a mathematical model to obtain the minimum time. (c) Solve this model using the Vogel's approximation model.