Need assistance with these problems! 1. The following is a linear programming fo

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Need assistance with these problems!

1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X1 + X2 + X3 + X4
Subject to: X1 + X4%u2265 12 (shift 1)
X1 + X2%u2265 15 (shift 2)
X2 + X3%u2265 16 (shift 3)
X3 + X4%u2265 14 (shift 4)
all variables %u2265 0

Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3)                                           12
                                        13
                                        0
                                        none of the above
                                            
                         

               
                         

               
                         

               
                         

               
                         

               
                         

               
                         

               
                         

               
                                             

                     2. When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and: (Points : 3)                                           finding the profit at every corner point of the feasible region to see which one gives the highest value.
                                        moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
                                        locating the point that is highest on the graph.
                                        none of the above.
                                        all of the above.
                         

Explanation / Answer

1. 12

2. finding the profit at every corner point of the feasible region to see which one gives the highest value.

3.parallel to

4.maximize profits from blends of nutrients

5.different product mix, same total profit as before.

6.requires that the profit from all corners of the feasible region be compared.

7.1200

8.choosing the options for assuming both a linear model and non-negative variables

9.(50,40)

10.Sensitivity analysis

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