Question

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by 32)

c = 4x2 - 368x + 82, where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

A) 46 watches B) 41 watches C) 40 watches D) 82 watches

Answer 1

He must need to repair 46 watches to have the lowest cost.

Explanation:

Consider the provided function.

`c = 4x^2 - 368x + 82`

Where c is cost and x is the number of watches repaired.

The coefficient of x² is a positive number, therefore the graph of the above function is an upward parabola.

The minimum point of the upward parabola lying on the vertex of the parabola.

The general form of a parabola's equation is:
`y=ax^2+bx+c`

We can find the x coordinate of the vertex by using the formula:
`x =(-b)/(2a)`

Now by comparing general form with provided function we can concluded that a=4, b=-368 and c=82

Now substitute the value of a=4 and b=-368 in above formula.

`x =(-(-368))/(2(4))`

`x =(368)/(8)`

`x =46`

Hence, he must need to repair 46 watches to have the lowest cost.