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
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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