3. (20 points) A textile manufacturing company is experiencing growth and considering best timing for the addition of extra capacity through building a new manufacturing plant. Based on their previous experience a plant with a capacity of 100,000 meters of fabric is costing $3M to build. Their systems engineer also did some analytics to figure out that doubling the size of an existing plant in its current location increases the plant establishment cost by 70%. The data show that the yearly demand is increasing at 30,000 meters and discount rate for future costs are estimated at 10%. a) Find the values for k and a assuming a cost relationship of the form f(y)=k*ya c) Determine the optimal timing the new plant and the plant capacity