Alunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. on a typical weekday, it sells between 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?

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 and the number of Caesar salad is

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

So, the two constraints are:   and  

The total number sold has never exceed 100 salads. So, another constraint will be:  

According to the graph of the constraints, the vertices of the common shaded region are:   and   (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:  

For  (40, 35) ,  

For  (60, 35) ,  

For  (60, 40) ,  

For  (50, 50) ,   (Maximum)

For  (40, 50) ,  

Profit will be maximum when and

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

x + 4/7

step-by-step explanation:

use cymath

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."