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Date May 2018 Marks available 2 Reference code 18M.1.SL.TZ2.T_13
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 2
Command term Find Question number T_13 Adapted from N/A

Question

A factory produces shirts. The cost, C, in Fijian dollars (FJD), of producing x shirts can be modelled by

C(x) = (x − 75)2 + 100.

The cost of production should not exceed 500 FJD. To do this the factory needs to produce at least 55 shirts and at most s shirts.

Find the cost of producing 70 shirts.

[2]
a.

Find the value of s.

[2]
b.

Find the number of shirts produced when the cost of production is lowest.

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

(70 − 75)2 + 100     (M1)

Note: Award (M1) for substituting in x = 70.

125     (A1) (C2)

[2 marks]

a.

(s − 75)2 + 100 = 500     (M1)

Note: Award (M1) for equating C(x) to 500. Accept an inequality instead of =.

OR

     (M1)

 

Note: Award (M1) for sketching correct graph(s).

(s =) 95    (A1) (C2)

[2 marks]

b.

     (M1)

Note: Award (M1) for an attempt at finding the minimum point using graph.

OR

95 + 55 2      (M1)

Note: Award (M1) for attempting to find the mid-point between their part (b) and 55.

OR

(C'(x) =) 2x − 150 = 0     (M1)

Note: Award (M1) for an attempt at differentiation that is correctly equated to zero.

75     (A1) (C2)

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 5 —Calculus » SL 5.8—Testing for max and min, optimisation. Points of inflexion
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Topic 5 —Calculus

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