$1.$ Sony Electronics hires Mr$.$ Mark Gunther of Brockhart & Kaitlin in order to manage inventory operations. Sony has a supplier that produces electronic circuit boards for its TV sets. Sony currently pays $$300$ for each circuit boards, and consumes an estimated $30,000$ boards in a year. It costs Sony $$700$ to place an order to its supplier. The unit inventory holding cost is estimated to be equal to $50\%$ of the purchasing price. Determine the economic order quantity for Sony$$s outsourcing alternative.

$2.$ Given the economic order quantity that you found for Question $1,$ calculate the associated annual total cost $($including ordering, inventory holding and purchasing costs$)$ for Sony$$s outsourcing alternative.

$3.$ Sony$$s engineers inform Mark Gunther that a new facility soon to be fully operational within the supply chain of the company can actually produce the same circuit boards $($of Problem $1).$ The unit manufacturing cost at this plant is estimated to be equal to $$295$ per board. The setup cost is equal to $$700.$ The plant is scheduled to work for $250$ days and has a daily demand of $120$ boards $($corresponding to an annual demand of $30,000)$ while having the capability of producing at a rate of $240$ boards$/$day$.$ As in the outsourcing alternative of Problem $1,$ the unit inventory holding cost is $50\%$ of the unit manufacturing cost. Compute the economic production quantity.

$4.$ Given the economic production quantity that you calculated for Question $3,$ find the associated annual total cost $($including setup, inventory holding and manufacturing costs$)$ for Sony$$s manufacturing alternative.

$5.$ Given your answers for question $2$ and question $4,$ determine whether Sony should choose outsourcing or manufacturing alternative. A$)$ Sony should choose manufacturing alternative B$)$ Sony should choose outsourcing alternative.

$6.$ The supplier Sony Electronics uses $($in Problem $1$ and $2)$ produces a new and updated price list based on increased order quantities. The following list shows the new prices: Using the same ordering cost information available in Problem $1,$ what is the optimal order quantity for Sony?

Order Quantity $1-499500-99910001499150019992000+$ Unit Price per Circuit Card $$300\mathrm{.}00$ $$297\mathrm{.}00$ $$294\mathrm{.}00$ $$291\mathrm{.}00290\mathrm{.}00$

$7.$ Using the same ordering cost information available in Problem $1,$ and the optimal order quantity for Sony in Problem $6,$ calculate the associated annual total cost for the outsourcing alternative with price discounts.

The answer to question $1$ is $529$ units, I need the solution and answer to the other parts of the problem. Thank you!