Alumco manufactures aluminum sheets and aluminum bars. The maximum production capacity is estimated at either 800 sheets or 600 bars per day. The maximum daily demand is 550 sheets and 560 bars. The profit per ton is $40 per sheet and $35 per bar. Determine the optimal daily production mix

Answer:The optimal daily production is 550 sheets and 387.5 bars.Step-by-step explanation:Let x be the no. of sheets Let y be the no. of bars The profit per ton is $40 per sheet and $35 per bar.So, Profit function = 40x+35yThe maximum daily demand is 550 sheets and 560 bars.So, [tex]x\leq 550\\y\leq 560[/tex]Now we are given that The maximum production capacity is estimated at either 800 sheets or 600 bars per daySo, equations becomes :[tex]\frac{600}{800}x+y\geq 600[/tex][tex]\frac{600}{800}x+y\leq 800[/tex]Plot the equations on the graph So, The points of feasible region are : (53.333,560),(320,560),(550,387.5) and (550,187.5)Profit function = 40x+35yAt(53.333,560)Profit  = 40(53.333)+35(560)=21733.32At (320,560)Profit  = 40(320)+35(560)=32400At (550,387.5)Profit  = 40(550)+35(387.5)=35562.5At (550,187.5)Profit  = 40(550)+35(187.5)=28562.5Since profit is maximum at (550,387.5)So,  the optimal daily production is 550 sheets and 387.5 bars.