Can someone help me with #3

2.2 Graphical LP Solution 17 The values of x, and x, associated with the optimum point Care deter- ned by solving the equations associated with lines (1) and (2)-that is 6x +4r-24 The solution is x1 = 3 and x2 = 1.5 with z = 5 x 3 + 4 x 1.5-21. This calls for a daily product mix of 3 tons of exterior paint and 1.5 tons of inte- rior paint. The associated daily profit is $21,000. It is not accidental that the optimum solution occurs at a corner point of the solution space where two lines intersect. Indeed, if we change the slope of the profit function z (by changing its coefficients), we will discover that the optimum solution always occurs at one of these corner points This obser- vation is key to the development of the general simplex algorithm presented in Chapter 3. PROBLEM SET 2.2A 1. Determine the feasible space for each of the following independent constraints given that x (a)3x1+x6 (c) 2 3t 12 (e)xx20 Identify the direction of increase in z in each of the following cases: (a) Maximize zx-x (b) Maximize z-5x,-6 (c) Maximize z=-x1+2x2 (d) Maximize z-3x Determine the solution space and the optimum solution of the Reddy Mikks model for each of the following independent changes (a) The maximum daily demand for exterior paint is at most 25 tons (b) The daily demand for interior paint is at least 2 tons (c) The daily demand for interior paint is exactly 1 ton higher than that for exterior 2. 3. paint. (d) The daily availability of raw material M1 is at least 24 tons (e) The daily availability of raw material M1 is at least 24 tons and the daily demand for interior paint exceeds that of exterior paint by at least 1 ton. 4. For the (original) Reddy Mikks model, identify the corner point(s) that define the opti- mum solution for each of the following objective functions (b) zx 3 (c) z = 6x1 + 4x2 How does the solution in (c) differ from those in (a) and (b)