# math homework due in 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 >= 5×2 – xs + y2 >= 3×3 – x1 + y3 >= 4×4 – x1 + y4 >= 6×5 – x2 + y5 >= 5×6 – x2 + y6 >= 7×7 – x3 + y7 >= 9×7 – x5 + y7 >= 9×8 – x4 + y8 >= 9×8 – x6 + y8 >= 8 