VTAARPS, Inc. currently sells a ‘Tailgating HID’ and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is p = $ 38 + (2700/D) − (5000/D^2) for D > 1 where p is the price per unit in dollars and D is the demand per month. VTAARPS, Inc. is seeking to maximize its profit. Its fixed cost is $1,000 per month and the cost for each HID is $40. What is the number of units that should be produced and sold each month to maximize profit? Show work and refrain from using Excel.