Suppose a linear program graph results in a number line for the binding constraints as follows: -3 -2/3 If the objective function is Max 5X1 + 10X2, what is the sensitivity range on C2? O C2 2 1.67 and C2 s 7.5 O C2 2 6.67 O C2 s 7.5 O C2> 75
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- 2. Consider the transportation problem having the following parameter table (M is a big positive number) Source Demand 1 12345 2 3 5 1 2 3 343800 13 14 4 18 3 0 130940 Destination 4 5 22 29 18 21 M 3 5 26M940 16 M 11 24 34 19 23 11 4 6 Supply 0 ooooo 0 6 0 0 36 28 0 5 6 2 56743 (a) Use the northwest corner rule manually to obtain a complete initial BF solution, also find the objective value for this solution. How many basic variables are there in this solution? (b) Use Vogel's approximation method manually to select the first basic variable for an initial BF solution. (Attention, do not need to find an complete initial BF solution, just find the first BV for this initial BF solution)Maximize Profit=123 L + 136 S 17 L+11 S≤ 3000 6 L+9 S≤2500 L20 and S20 (Availability of component A) (Availability of component B) Show Transcribed Text Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and SpeedBuster models. This solution gives the possible profit, which is $. (Type integers or decimals rounded to two decimal places as needed.)An investor is looking to invest R 250,000 with the intent of getting the highest possible return. He plans to do this by holding a diverse stock portfolio with different hypothetical stocks with varying expected returns as seen in the table below. Stock Return earned Naspers 6% Sasol 15% ABSA 9. Capitec 3% To control for risk, the following constraints are put into place: a) No more than 15% of the total investment can be put into ABSA stocks. b) At most 40% must be invested in Sasol stocks and the Capitec stocks combined. c) The amount put in Naspers stocks must be no more than the amount invested into all the other remaining stocks combined. d) All the R250,000 must be invested and no shorting is allowed. Formulate a linear programming model for this problem to get the highest return (i.e., Define and outline your decision variables, objective function and constraints). How much of the budget should be invested into each investment option? (Show your workings in Microsoft Excel)