Question $1(25$ points$)$ Guelph Kit produces three products: DIZ, GEF and JIQ. Unit data for the three products is as follows: All three products use the same direct material, Avriz, which costs $\backslash (\backslash$$ $6\backslash )$ per pound and a maximum of $17,600$ pounds is available each month. The monthly demand for DIZ, GEF and JIQ is $1,200$ units, $1,000$ units and $800$ units respectively. The fixed costs per unit are calculated based on the current production capacity, which cannot be changed in the short run. With this capacity, the company can produce $2,500$ units of the three product each month. Required: $1)$ Given the constraint represented by the available material, rank the three products in the order in which they will be produced to maximize the company's operating income. $[13$ marks$]2)$ How many units of product DIZ, GEF and JIQ should the company produce? $[7$ marks$]2)$ What is the maximum amount $($per pound$)$ the company would be willing to pay for another $420$ pounds of Avriz? $[5$ marks$]$