1 of 8 0-day streak

Model and solve constrained optimisation problems

Question 1 of 8

No calculator

Distinguish the input that optimises the model from the maximum output itself

A processing model predicts usable output Y grams after a duration t minutes. Treat time as continuous and optimise only over the stated valid interval

Y(t)=-3t^{2}+12t+108

0\le t\le4

The displayed interval is the full valid model domain

(a)1 mark

Which candidate plan respects the model and the stated domain?

Compare both included endpoints and every stationary input that lies inside the interval

Compare only the endpoints in every problem, even when stationary inputs lie inside the domain

Use the stationary input even if the domain excludes it

Maximise the derivative instead of the output

(b)2 marks

Enter every coefficient in descending powers, including zero for an absent term

Y'(t)=A_1t+A_0

\(\text{coefficient of }t\) \(\text{constant coefficient}\)

Enter the positive stationary input of the polynomial model (even if outside the permitted interval), then the exact values at the two included endpoints

\(t_*\) \(Y(0)\) \(Y(4)\)

(d)2 marks

Enter the optimiser in minutes, the maximum output in grams

\(t_{\max}\) \(Y_{\max}\)

(e)1 mark

Which conclusion correctly interprets the constrained result?

The maximum is \(120\) grams at \(t=2\) minutes

The unrestricted stationary input is always the constrained optimiser, even when excluded

The maximum output equals the optimiser 2 grams

No endpoint can attain a constrained maximum