mat - 0135c - le02\nveronica kargbo | 04/03/25 4:01 pm\n< 9 of 20 > this test: 20 point(s) possible this…

mat - 0135c - le02\nveronica kargbo | 04/03/25 4:01 pm\n< 9 of 20 > this test: 20 point(s) possible this question: 1 point(s) possible submit\nthe marginal cost of a product can be thought of as the cost of producing one additional unit of output. for example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase production from 49 to 50 units of output. suppose the marginal cost c (in dollars) to produce x thousand mp3 players is given by the function c(x)=x² - 160x + 7500.\na. how many players should be produced to minimize the marginal cost?\nb. what is the minimum marginal cost?\na. to minimize the marginal cost, □ thousand mp3 players should be produced\nb. the minimum marginal cost is $□

mat - 0135c - le02\nveronica kargbo | 04/03/25 4:01 pm\n< 9 of 20 > this test: 20 point(s) possible this question: 1 point(s) possible submit\nthe marginal cost of a product can be thought of as the cost of producing one additional unit of output. for example, if the marginal cost of producing the 50th product is $6.20, it cost $6.20 to increase production from 49 to 50 units of output. suppose the marginal cost c (in dollars) to produce x thousand mp3 players is given by the function c(x)=x² - 160x + 7500.\na. how many players should be produced to minimize the marginal cost?\nb. what is the minimum marginal cost?\na. to minimize the marginal cost, □ thousand mp3 players should be produced\nb. the minimum marginal cost is $□

Answer

Explanation:

Step1: Identify the function type

The cost function $C(x)=x^{2}-160x + 7500$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a = 1$, $b=-160$, $c = 7500$.

Step2: Find the x - value of the vertex

For a quadratic function $y=ax^{2}+bx + c$, the x - value of the vertex (which gives the minimum for $a>0$) is $x=-\frac{b}{2a}$. Substitute $a = 1$ and $b=-160$ into the formula: $x=-\frac{-160}{2\times1}=80$.

Step3: Find the minimum cost

Substitute $x = 80$ into the cost function $C(x)$. $C(80)=80^{2}-160\times80 + 7500=6400-12800 + 7500=1100$.

Answer:

A. 80 B. 1100