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+35y
The 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 day
So, 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+35y
At(53.333,560)
Profit = 40(53.333)+35(560)=21733.32
At (320,560)
Profit = 40(320)+35(560)=32400
At (550,387.5)
Profit = 40(550)+35(387.5)=35562.5
At (550,187.5)
Profit = 40(550)+35(187.5)=28562.5
Since profit is maximum at (550,387.5)
So, the optimal daily production is 550 sheets and 387.5 bars.
