maths assignment due i 2 hours

To formulate the linear model, we first need to find out the crash costs per week. This is calculated using the formula (Crash cost - Normal Cost) / (Normal time - Crash time). This is calculated for each of the activities as shown belowThe variables that considered for are belowLet xi (i = 1 to 8) be the earliest start time of each activity andyi (i = 1 to 8) be the crash times for each activity. xs and xf are the start and finish time.The objective function is to minimize the total crash cost. This can be represented asMinimize : 6y1 + 12y2 + 4y3 + 6.67y4 + 10y5 + 7.3y6 + 5.75y7 + 8y8subject to constraintsy1 < 2 (2 is the maximum time activity 1 can be crashed = 5-3 =2. similarly for all activities)y2 < 1y3 < 2y4 < 3y5 < 1y6 < 3y7 < 4y8 < 2xf < 15 (The constraint for finish time after crashing)xs = 0 (Constraint for start time = 0)The constraint of crashing can be represented asx1 - xs + y1 >= 5x2 - xs + y2 >= 3x3 - x1 + y3 >= 4x4 - x1 + y4 >= 6x5 - x2 + y5 >= 5x6 - x2 + y6 >= 7x7 - x3 + y7 >= 9x7 - x5 + y7 >= 9x8 - x4 + y8 >= 9x8 - x6 + y8 >= 8