| Date | May 2018 | Marks available | 2 | Reference code | 18M.1.sl.TZ2.13 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 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.
Find the value of s.
Find the number of shirts produced when the cost of production is lowest.
Markscheme
(70 − 75)2 + 100 (M1)
Note: Award (M1) for substituting in x = 70.
125 (A1) (C2)
[2 marks]
(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]
(M1)
Note: Award (M1) for an attempt at finding the minimum point using graph.
OR
\(\frac{{95 + 55}}{2}\) (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]
