Answer to Question #303233 in Algebra for Dima

Question

The production cost, represented by y, of smart phone devices are equal to the product of computing components a and the square of the number of devices x, added to the product pf labour b and number of devices x; after which savings on reusable material c are subtracted.

2.1. Suppose the production cost is R 239250, computing components cost is R1035, labour cost is R4140 and the savings on reusable materials is R1725, determine the number of devices produced

2.2. Hence, write down the equation with y as subject (in terms of x) to represent the production cost.( the value of a, b and c must be indicated.

Answer 1

2.1) 

$$y=ax^2+bx-c$$

2.2

$$y=239250$$

$$a=1035$$

$$b=4140$$

$$c=1725$$

$$1035x^2+4140x-240975=0, x>0$$

$$23x^2+92x-5355=0$$

$$x=\dfrac{-46\pm\sqrt{46^2+23(5355)}}{23}$$

Since $x>0,$ we take

$$x=\dfrac{-46+\sqrt{46^2+23(5355)}}{23}$$

$$x=13$$

2.2

$$y=1035x^2+4140x-1725, x>0$$