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Supertronics, Inc., would like to know how the profitability is altered by product mix. Currently, the product mix is determined by giving priority to the product with the highest per$-$unit contribution margin$($defined as the difference between price and material cost$).$ Details on the Supertronics product line, including processing time at each workstation, follow: PRODUCT Alpha Beta Delta GammaPrice $$350\mathrm{.}00$ $$320\mathrm{.}00$ $$400\mathrm{.}00$ $$500\mathrm{.}00$Material Cost $$50\mathrm{.}00$ $$40\mathrm{.}00$ $$125\mathrm{.}00$ $$150\mathrm{.}00$Weekly Demand in Units $100605080$Processing Time at Machine $1$ in Minutes$2004010$Processing Time at Machine $2$ in Minutes$2520050$Processing Time at Machine $3$ in Minutes$0206030$a$.$ Assume that Supertronics has $5,500$ minutes of capacity available at each workstation each week. Develop a linear program to define the production mix that maximizes contribution margin. b$.$ Solve your formulation using a computer package such as POM for Windows. c$.$ Given your solution for part $($b$),$ which machine is the bottleneck?