The Buffalo plant can produce $2000$ units of component $1,1000$ units of component $2,$ or any combination of the two components each day. For instance, $60\%$ of Buffalo$$s production time could be used to produce component $1$ and $40\%$ of Buffalo$$s production time could be used to produce component $2$; in this case, the Buffalo plant would be able to produce $0\mathrm{.}6(2000)51200$ units of component $1$ each day and $0\mathrm{.}4(1000)5400$ units of component $2$ each day. The Dayton plant can produce $600$ units of component $1,1400$ units of component $2,$ or any combination of the two components each day. At the end of each day, the component production at Buffalo and Dayton is sent to Cleveland for assembly of the ignition systems on the following workday. LO $2,4,5$

a$.$ Formulate a linear programming model that can be used to develop a daily production schedule for the Buffalo and Dayton plants that will maximize daily production of ignition systems at Cleveland.

b$.$ Find the optimal solution.