The production cost of a batch of cooking sauce is given by the formula $y = 2x^2 - 18x + 75$ wher

Question

The production cost of a batch of cooking sauce is given by the formula $y = 2x^2 - 18x + 75$ where $y$ represents production costs and $x$ represents the number of production units in litres. Corresponding values of $x$ and $y$ are given in the table below.

$x$ (litres)	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$y$ (dollars)	$75$	$59$	$a$	$39$	$35$	$35$	$39$

Calculate the value of $a$.
[1]
Explain the significance of the value of $y$ when $x = 0$
[1]
Using a scale of $2$ cm to represent $1$ unit on the $x$-axis and $2$ cm to represent $10$ units on the $y$-axis, draw the graph of $y$ against $x$ for $0 \leq x \leq 6$.
[3]
Use the graph to find
1. the production cost when $x = 2.5$,
  [1]
2. the number of litres so that the production cost is the lowest,
  [1]
3. the range of values of $x$ if the production cost is to be kept below $\$38$.
  [1]
If the production cost is increased by $15\%$ due to rising fuel costs, write down a quadratic function in the form $y = ax^2 + bx + c$ to represent this information.
[1]

Accepted Answer

(a) $47$. (b) Fixed production cost $\$75$. (c) Graph shown. (d)(i) Approximately $\$42.5$. (ii) Approximately $4.5$ litres. (iii) Approximately $3.2<x<5.8$; exact boundaries $\dfrac{9-\sqrt7}{2}<x<\dfrac{9+\sqrt7}{2}$. (e) $y=2.3x^2-20.7x+86.25$.

2022 ACSI EOY P2 Q3

2022 ACSI EOY P2 Q3

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