A company produces three types of electronic products: Headphones, Gaming Controllers and Bluetooth

Question

A company produces three types of electronic products: Headphones, Gaming Controllers and Bluetooth Speakers. The total manufacturing cost of $5$ Headphones, $6$ Gaming Controllers and $10$ Bluetooth Speakers is $\$1400$. The total manufacturing cost of a Headphone and a Gaming Controller is twice the manufacturing cost price of a Bluetooth Speaker. The total manufacturing cost of $10$ Gaming Controllers is $\$131.25$ more than the total cost of $5$ Headphones and $5$ Bluetooth Speakers. By writing down three linear equations, find the manufacturing cost of one Headphone.[4] An economist advises the company on how to increase their profit.$$\text{Profit} = \text{selling price} - \text{manufacturing cost}$$ In a simple model, the economist suggested that the electronic products should be priced at $\$80$ per electronic product. Find the profit from the sale of $70$ of each of Headphones, Gaming Controllers and Bluetooth Speakers.[2] The company is trialing a new type of product, Wireless Earbuds. The economist predicts that the profit $\$P$ will be related to the manufacturing cost ($\$x$) by the equation $$P = 6\sqrt{x} - 0.8x$$ Sketch the graph of $P$ against $x$, stating the coordinates of the points of intersection with the $x$-axis.[2] Use your calculator to estimate the maximum value of $P$. State also the value of $x$ for which this maximum value occurs.[2] Given that the manufacturing cost of a pair of Wireless Earbuds is $\$40$, find the selling price.[2]

Accepted Answer

(i)$57.50 (ii)$2887.50 (iv)Max profit = $$ 11.25 $ when x = $ 14.06 (v)$45.95

2204 ASRJC H1 Q5

2204 ASRJC H1 Q5