If you can please show the step by step process to solve this problem

3. (35 pts.) A start-up needs to determine the production capacity in pounds per month to deploy at a new lab. They want to match production to demand in each month, to avoid shortages and inventory accumulation. An option being considered: Any excess demand that cannot be met through the planned capacity will have to be met through overtime, at the differential cost of $100 per pound. The accounting department, however, estimates that under-utilized capacity implies an opportunity cost of $200 per pound. If monthly demand is expected to be normally distributed with a mean of 100,000 pounds and a standard deviation of 5,000 pounds, what is an optimal selection of the lab capacity, based on the above information