The cost C in dollars for a company to produce and sell x th

The cost C (in dollars) for a company to produce and sell x thousand gadgets is given by C =1/50 x^2 - 2x + 2050 What is the company\'s start-up cost? What is the minimum cost? How many gadgets must the company produce and sell in order to incur the least cost? (Be careful with your units!)

Solution

The cost C = (1/50)x² - 2x + 2050.

(a).The constant in the cost function, i.e. $ 2050 is the start up cost.

(b) The minimum cost is when there is no variable cost, i.e. when x = 0. Thus, the minimum cost is the same as the start up cost, i.e,.$ 2050

(c) If there is production of x units, then the cost is least when (1/50)x² - 2x = 0 or., x² - 100x = 0 or, x ( x-100) = 0 Then either x = 0, i.e., there is no production, or when x = 100 , i.e. when 100 units are produced. Under both these circumstances, the cost is least ($ 2050) . Since the question is about the number of units produced and sold, the answer is 100 gadgets.