This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — Here are the solutions to the problems. Question 1.1 1.1.1 Use the information above to write down inequalities associated with the lines represented by f and h. The feasible region is the shaded area. • Line f passes through points (0, 45) and (40, 5). Step 1: Find the slope (m) of line f. m = (y_2 - y_1)/(x_2 - x_1) = (5 - 45)/(40 - 0) = (-40)/(40) = -1 Step 2: Use the point-slope form y - y_1 = m(x - x_1) with point (0, 45). y - 45 = -1(x - 0) y - 45 = -x y = -x + 45 x + y = 45 Since the feasible region is below or on line f, the inequality is x+y 45. • Line h is a horizontal line passing through point B and C. From point C (20, 25), we know y=25. From point B, the y-coordinate is also 25. The line h is y=25. The feasible region is below or on line h, so the inequality is y 25. However, the problem states "Given is the constraint 5 y 25". This means y 5 and y 25. Line h is y=25. The feasible region is below or on this line. So, y 25. The line g is y=5. The feasible region is above or on this line. So, y 5. The question asks for inequalities associated with lines f and h. The inequality for line f is x+y 45. The inequality for line h is y 25. **1.1.2