In a manufacturing process that involves a single machine, decisions must be made on whether to deliver the product to the customer immediately upon completion of the job or to hold the finished product in a batch with other jobs to be delivered at a later time. A computerized mathematical model for solving the batch scheduling problem was proposed in the Asian Journal of Industrial Engineering (Vol. 4, 2012). The performance of the model was graded using a variable called Value of Object Function (VOF). Simulation yielded the following data on VOF and run time (in seconds) for six software runs, each run with a different number of held batches.

a. Use simple linear regression to estimate the equation, y = β_o + β₁x + ∈, where y = VOF and x = number of batches.

b. Find an estimate of σ² = V(∈), and σ = √V(∈). 

c. Which of the two estimates, part b, can be practically interpreted? Give the interpretation.

SWRUN Software Number of VOF Run Time Run Batches (seconds) 1 3 86.68 27 2 4 232.87 14 5 372.36 12 4 6. 496.51 18 5 7 838.82 42 6 8 1183.00 33 3.