Question $1(10$ Points$)-($SHOW ALL POSSIBLE WORK!!$)$ Maxwell Manufacturing makes two models of felt tip marking pens. Each box of pens requires $3$ inputs to production: Plastic, Ink Assembly, and Molding Time. The number of units of each input required for each box of each pen model are given below. The number of total available units of each input is also provided. Input Fliptop Model Tiptop Model Available Plastic $3436$ Ink Assembly $5440$ Molding Time $5230$ The profit for either model is $$1000$ per box. Hints: there are three constraints, one for each input. Each input is a function of two variables, the number of boxes of Fliptop and Tiptop models produced. $1.$ What is the linear programming model for this problem? $2.$ Find the optimal solution. $3.$ Will there be excess capacity in any input? In other words, will there be leftover units of Plastic, Ink Assembly, and$/$or Molding Time? $4.$ Submit an Excel Document with Your Template