Math, asked by mihirparida1518, 10 months ago

The cost of hiring a catering service to service to service for a party is 150 pesos per head for 20 persons or less, 130 pesos per head for 21 to 50 persons, and 110 pesos per head for 51 to100 persons. for 100 or more persons the cost is that 100 pesos per head. represent the total cost as a piecewise function of the number of attendees of the party

Answers

Answered by amitnrw
15

Given :        The cost of hiring a catering service to service to service for a party is 150 pesos per head for 20 persons or less, 130 pesos per head for 21 to 50 persons, and 110 pesos per head for 51 to100 persons. for 100 or more persons the cost is that 100 pesos per head.

To Find : represent the total cost as a piecewise function of the number of attendees of the party

Solution:

150 pesos per head for 20 persons or less,

Let say x represent number of attendees of the party

f(x) represent cost

person can not be zero or less than that

f(x)  = 150x    for  0 <  x  ≤ 20

cost for 20 person = 150 * 20 = 3000

130 pesos per head for 21 to 50 persons,

f(x) = 3000 + 130(x - 20)  =  130x  + 400

f(x) =  130x  + 400    for  20 <  x  ≤ 50

f(50) = 6900

110 pesos per head for 51 to 100 persons,

f(x) = 6900 + 110(x - 50)  =  110x  + 1400

f(x) =  110x  + 1400     for  50 <  x  ≤ 100

f(100) = 12400

100 pesos per head for > 100 persons,

f(x) = 12400 + 100(x - 100)  =  100x  + 2400

f(x) =  100x  + 2400     for    100 <  x

Piece wise function is :

150x    for  0 <  x  ≤ 20

130x  + 400    for  20 <  x  ≤ 50

110x  + 1400     for  50 <  x  ≤ 100

100x + 2400     for    100 <  x

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