Montpelier is planning its production of skis for the months of July, August, and September. Production capacity and unit production cost will change from month to month. Production levels should meet both demand forecasts and end-of-quarter inventory requirement in every month. Skis can be stored in a warehouse to satisfy demand in later months. An inventory holding cost will be incurred in that case. Initial inventory at the beginning of July = 200 pairs. Ending inventory required at the end of September =800 pairs. Holding cost per month per ski is $0.5.Month Demand Production Capacity Unit Production CostJuly 300 1000 25August 500 800 26September 700 400 29Management would like to schedule production to minimize its costs for the quarter.(a) Formulate the problem mathematically by clearly defining the decision variables, objective function and constraints.(b) Implement this problem in excel to solve for the optimal solution.