1 of 8 0-day streak

Model and solve constrained optimisation problems

Question 1 of 8

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Two non-negative dimensions add to \(18\,\mathrm{m}\). The product of the dimensions must be maximised

Let \(w\) be the first length and \(l\) the second length

w+l=18

A(w,l)=wl

The practical domain is \(w\in\left[0,18\right]\)

Use the practical domain and the derivative to obtain the answer

(a)1 mark

Select the correct one-variable objective after using the displayed data

A(w)=18-w

A(w)=-w^{2} + 18\,w

A(w,l)=wl

(b)4 marks

Complete the numerical table for the constraint and the one-variable objective

Given constant in the constraint coefficient of w to the power 2 coefficient of w constant term

Select the practical domain for \(w\)

w\in\left[0,36\right]

w\in\left[0,18\right]

w\in\mathbb{R}

(d)6 marks

Complete the candidate table. Enter every stationary input and the objective value at each listed input

Left endpoint input Objective at the left endpoint Stationary input 1 Objective at stationary input 1 Right endpoint input Objective at the right endpoint

(e)1 mark

Find the input value \(w\) that gives the stated maximum

Optimal value of w (metres)

Format: Exact value

(f)1 mark

Find the maximum objective value

maximum objective value (square metres)

Format: Exact value