Question

C. The cost of hiring a catering service to serve food for a party is P250.00 per
head for 50 persons or less, P200.00 per head for 51 to 100 persons, and
P150.00 per head for more than 100. Represent the total cost as a piecewise
function of the number of attendees to the party.
15​

Answer 1

Given :- The cost of hiring a catering service to serve food for a party is :-

• P250.00 per head for 50 persons or less.
• P200.00 per head for 51 to 100 persons.
• P150.00 per head for more than 100.

Represent the total cost as a piecewise function of the number of attendees to the party.

Solution :-

Let us assume that, f(x) represent the cost function and x represent the number of persons.

1) P250.00 per head for 50 persons or less :-

→ f(x) = 250 * x for 0 < x ≤ 50 .

and,

→ f(20) = 250 * 50 = P12,500.00

2) P200.00 per head for 51 to 100 persons :-

→ f(x) = 12500 + 200(x - 50)

→ f(x) = 12500 + 200x - 10000

→ f(x) = 2500 + 200x for 50 < x ≤ 100.

and,

→ f(100) = 2500 + 200 * 100

→ f(100) = 2500 + 20000 = P22,500.00

3) P150.00 per head for more than 100.

→ f(x) = 22500 + 150(x - 100)

→ f(x) = 22500 + 150x - 15000

→ f(x) = 7500 + 150x for 100 < x.

Therefore,

Piecewise function of the number of attendees to the party :-

→ f(x) = 250 * x for 0 < x ≤ 50 .

→ f(x) = 2500 + 200x for 50 < x ≤ 100.

→ f(x) = 7500 + 150x for 100 < x.

Answer 2

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Given :-

The cost of hiring a catering service to serve food for a party is :-

P250.00 per head for 50 persons or less.

P200.00 per head for 51 to 100 persons.

P150.00 per head for more than 100.

Represent the total cost as a piecewise function of the number of attendees to the party.

Solution :-

Let us assume that, f(x) represent the cost function and x represent the number of persons.

1) P250.00 per head for 50 persons or less :-

→ f(x) = 250 * x for 0 < x ≤ 50 .

and,

→ f(20) = 250 * 50 = P12,500.00

2) P200.00 per head for 51 to 100 persons :-

→ f(x) = 12500 + 200(x - 50)

→ f(x) = 12500 + 200x - 10000

→ f(x) = 2500 + 200x for 50 < x ≤ 100.

and,

→ f(100) = 2500 + 200 * 100

→ f(100) = 2500 + 20000 = P22,500.00

3) P150.00 per head for more than 100.

→ f(x) = 22500 + 150(x - 100)

→ f(x) = 22500 + 150x - 15000

→ f(x) = 7500 + 150x for 100 < x.

Therefore,

Piecewise function of the number of attendees to the party :-

→ f(x) = 250 * x for 0 < x ≤ 50 .

→ f(x) = 2500 + 200x for 50 < x ≤ 100.

→ f(x) = 7500 + 150x for 100 < x.

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