$1.$ ?A Utility company with $2$ ?plants $(15$ ?points $)$ ?Recall that in Unit $2$ ?we also had the following extension of the one $-$ plant Utility Company problem: Suppose that the Utility Company is considering the possibility of building a second $($ more efficient $)$ ?plant. Specifically, the cost of its existing plant, now called Plant $1,$ ?and the cost of the new plant, now called Plant $2,$ ?are given below: Plant $110,050+5$ Q $22$ ?Plant $25,000+2$ Q $,$ ?where Q $,$ ?and Q $,$ ?denote the respective kilowatts produced at the respective plants. Thus, Q $=$ ?Q $,+$ Q $,$ ?What are the optimal production levels and optimal profit level? Hint: See Unit $6$ ?Practice Problem # $1$ ?& $2($ a $)$ ?Formulate as an algebraic optimization model. $($ Submit copy of Handwritten answer, $5$ ?pts $)($ b $)$ ?Create Excel model using your model from part $($ a $).($ Submit answer in an Excel file, $5$ ?pts $)($ c $)$ ?Then solve for the optimal output levels and optimal profit. $($ Submit answer in an Excel file, $5$ ?pts $)$