Please show work.

Think of yourself as a Big Mall entrepreneur who sells 1,000 cupcakes a day for $3 each. When you raised the price to $4.00 each, the sale plummeted to 900 cupcakes a day. Now, let's say there's a linear relationship between the price and the number of cupcakes sold. Furthermore, assume that there is a fixed cost (overhead) of $500 per day and the cost of each cupcake is 51.50. What would be the price ofa cake for maximum prot? {Hint: First determine the linear relationship of the number of units sold per day In} to the unit price {it}. Once you have n in terms of x, the profit y = Income [from selling cakes) cost overhead. The task is to find I: for maximum y.)