| Date | May Specimen | Marks available | 2 | Reference code | SPM.1.sl.TZ0.15 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
A small manufacturing company makes and sells x machines each month. The monthly cost C , in dollars, of making x machines is given by
C(x)=2600+0.4x2.The monthly income I , in dollars, obtained by selling x machines is given by
I(x)=150x−0.6x2.P(x) is the monthly profit obtained by selling x machines.
Find P(x) .
Find the number of machines that should be made and sold each month to maximize P(x) .
Use your answer to part (b) to find the selling price of each machine in order to maximize P(x) .
Markscheme
P(x)=I(x)−C(x) (M1)
=−x2+150x−2600 (A1) (C2)
−2x+150=0 (M1)
Note: Award (M1) for setting P′(x)=0 .
OR
Award (M1) for sketch of P(x) and maximum point identified. (M1)
x=75 (A1)(ft) (C2)
Note: Follow through from their answer to part (a).
787575 (M1)
Note: Award (M1) for 7875 seen.
=105 (A1)(ft) (C2)
Note: Follow through from their answer to part (b).
