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MAXImum [283]
3 years ago
9

a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet

ween 40 and 60 chefs salads and between 35 and 50 caesar salads. the total number sold has never exceed 100 salads. how many of each type should be prepared in order to maximize profit?

Mathematics
1 answer:
tangare [24]3 years ago
6 0

Answer:

<em>50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.</em>

Step-by-step explanation:

Suppose, the number of Chef's salad is x and the number of Caesar salad is y

On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.

So, the two constraints are:  40\leq x\leq 60 and  35\leq y\leq 50

The total number sold has never exceed 100 salads. So, another constraint will be:   x+y\leq 100

According to the graph of the constraints, the vertices of the common shaded region are:  (40,35), (60,35), (60,40), (50,50) and (40,50)   <em>(Refer to the attached image for the graph)</em>

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:  P=0.75x+1.20y

For  (40, 35) ,   P=0.75(40)+1.20(35)=72

For  (60, 35) ,   P=0.75(60)+1.20(35)=87

For  (60, 40) ,   P=0.75(60)+1.20(40)=93

For  (50, 50) ,   P=0.75(50)+1.20(50)=97.5 <u><em>(Maximum)</em></u>

For  (40, 50) ,   P=0.75(40)+1.20(50)=90

Profit will be maximum when x=50 and y=50

Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

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