Use the steps provided to solve these Linear Programming models provided. Make sure you solve the problems manually showing all the steps required. PROBLEM #1 Maximize 43x s.t. 45X + 18X + + 578 24YS 2875 360 252 X, Y IV FEASIBLE REGION Mark the outside of the Feasible Region (FR). This should be done with a heavy line that completely encloses the region. (The Feasible Region is the area of the graph that includes the area where all the areas that make the inequalities true overlap.) Identify cach corner of the Feasible Region with a capitalized letter - beginning with the letter A. (If the problem is a maximization problem, begin at the origin or closest to it and proceed in a clockwise direction. The origin will be Comer Point A, move up the Y-axis to the next Corner Point and mark it with a B, and so on. If the problem is a minimization problem, begin as far out the X axis as possible and begin with the Comer Point A and still proceed in a clockwise direction to the next Corner Point, mark with a B and so on.) If the Corner Point coordinates are not known, you must use an Algebraic solution to solve the problem and determine the coordinates of the Corner Point. (Take the two constraints that are involved in the intersection of the linear constraints and make both of the constraints equal to zero. Then set the constraints equal to each other and solve for each of the variables. This may take several steps!) 5. OBJECTIVE FUNCTION Take the coordinates of each of the Comer Points and plug into the objective function and calculate the result. The Corner Point that generates the number that matches the purpose of the Objective Function (Maximize or Minimize) is the solution to the problem. (For example, if the problem concerns the manufacture of two products by a small production firm, the solution determined by the coordinates of the Corner Point (the maximum amount) indicates the number of each of the products that should be manufactured in order to maximize the profit.) WRITE A BRIEF CONCLUSION In the conclusion, indicate the number of items that should be made or mixed together to generate the amount of the solution indicated by the number of the solution of the objective function. An example of a maximization production problem is listed below. If the coordinates of the Corner Point that solves the problem is 50, 30, the conclusion would be: In order to maximize the profit the company needs to generate 50 units of X and 30 units of Y during the next production period. By producing this quantity, the company will realize a profit of