Answer:
50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.
Step-by-step explanation:
Suppose, the number of Chef's salad is [tex]x[/tex] and the number of Caesar salad is [tex]y[/tex]
On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.
So, the two constraints are: [tex]40\leq x\leq 60[/tex] and [tex]35\leq y\leq 50[/tex]
The total number sold has never exceed 100 salads. So, another constraint will be: [tex]x+y\leq 100[/tex]
According to the graph of the constraints, the vertices of the common shaded region are: [tex](40,35), (60,35), (60,40), (50,50)[/tex] and [tex](40,50)[/tex] (Refer to the attached image for the graph)
The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be: [tex]P=0.75x+1.20y[/tex]
For (40, 35) , [tex]P=0.75(40)+1.20(35)=72[/tex]
For (60, 35) , [tex]P=0.75(60)+1.20(35)=87[/tex]
For (60, 40) , [tex]P=0.75(60)+1.20(40)=93[/tex]
For (50, 50) , [tex]P=0.75(50)+1.20(50)=97.5[/tex] (Maximum)
For (40, 50) , [tex]P=0.75(40)+1.20(50)=90[/tex]
Profit will be maximum when [tex]x=50[/tex] and [tex]y=50[/tex]
Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.
