Question $17(10$ points$)$

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A manager must decide on the mix of products to produce for the coming week. The product requires three jobs: cutting, stiching, and packing. Product A requires three minutes per unit for cutting, three minutes per unit for stiching, and one minutes for packing. Product B requires two minutes per unit for cutting, four minutes for stiching, and two minutes per unit for packing. There will be $480$ minutes available for cutting, $600$ minutes for stiching, and $520$ minutes for packing. Product A profit is $$25$ per unit and product B profit is $$30$ per unit.

a$.$ Define decision variables for this problem. $[3$ points$]$

b$.$ Define the objective function for this problem. $[3$ points$]$

c$.$ Define constraints for this problem. $[4$ points$]$