1. A State Fish and Game Department supplies three types of food to take to a lake that supports four species of fish. The following matrix represents the weekly average need of foods for each fish. For example, the 5 means that each fish of Species 2 consumes,each week, an average of 5 units of Food 3. Suppose each week 25,000 units of Food 1, 20,000 units of Food 2, and 40,000 units of Food 3 are supplied to the lake. Assume that all the food is eaten. a) On paper, set up a system of equations where the unknowns x1, x2, . are the numbers of each species of fish. b) Find the augmented matrix of the system, enter the matrix into Matlab, and use the rref command. Write the solution in terms of free variables in matrix form. c) Assume that each unknown (number of fish of each species) is non-negative (i.e.Xi > 0), find restriction(s) on the values of the free variables. On paper, describe how such restrictions affect the values of the other unknowns d) Determine the number of solutions in the solution set under the assumption in part (c).

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