StartLayout Enlarged left-brace 1st row negative 10 x squared minus 10 y squared = negative 300 2nd row 5 x squared + 5 y square
1 answer:
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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 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
<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:
For (40, 35) ,
For (60, 35) ,
For (60, 40) ,
For (50, 50) , <u><em>(Maximum)</em></u>
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.
Answer: P(t) = 1.25.sin(.t) + 5.65
Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:
y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D
where:
A is amplitude A=|A|
B is related to the period by: T =
C is the phase shift or horizontal shift:
D is the vertical shift
In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.
<u>Amplitude</u>:
a =
At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:
a =
a = 1.25
<u>b</u>
A time period for Pluto is T=66 years:
66 =
b =
<u>Vertical</u> <u>Shift</u>
It can be calculated as:
d =
d =
d = 5.65
Knowing a, b and d, substitute in the equivalent positions and find P(t).
P(t) = a.sin(b.t) + d
P(t) = 1.25.sin(.t) + 5.65
The Pluto's distance from the sun as a function of time is
P(t) = 1.25.sin(.t) + 5.65