Question 1 Inventory Simulation [50 points] 1.1 (15 points) For a given (postulated) pair of production and demand distribution models, we want to estimate certain characteristics of the single-item inventory model based on simulated inventory balance equations over a sequence of weeks. Input data: Weekly production distribution: Uniform(60, 90) Weekly demand distribution: Normal(75,15) Inventory at the beginning of week 1: 10 items No. of weeks simulated: 50 Inventory balance equation, for each week: Ending inventory = Beginning inventory + Production - Units sold Observe that the number of units sold either equals the demand or the available inventory (whichever is smaller). 1.2 (15 points) We want to estimate the following quantities: average and standard deviation of the beginning inventory, production, demand, and units sold; we also estimate the stockout probability. Create the graphs of the following quantities as these evolve over 50 weeks: beginning inventory, production, demand, units sold, and ending inventory. 1.3 (5*4 = 20 points) Describe shortly the expected effect of changing the input parameters indicated below. Production distribution: Uniform(Min, Max) Demand distribution: Nonnal(Mean. Sthev) Beginning inventory Add your brief answer to question 1.3 to your Excel le. E.g., if parameter Min increases, then