Question

The cost of producing 6000 face masks is $25,600 and the cost of producing 6500 face masks is $25.775. Use this information to create a function C (a) that represents the cost in dollars a company spends to manufacture x thousand face masks during a month. The linear equation is: C (x) = ____________

The vertical intercept for this graph is at the point ____________ (type a point) and represents a cost of $ ___________when a quantity of _________face masks are produced. The rate of change for C(a) is __________and means the cost is Based on this model, C(11) = ________ which means that when a quantity of ____________ face marks are produced, there is a cost of $ _________
Solving C (a)= 90, 700 shows x = ___________ which represents that for a cost of $. you can produce _____ face masks The appropriate domain of this function is ________ (interval notation- use INF for infinity if needed).

Answer 1

The cost of producing 6000 face masks is $25,600, and the cost of producing 6500 face masks is $25,775. We can use this information to find the slope of the line that represents the cost of producing face masks. The slope is the change in cost divided by the change in the number of face masks produced:
slope = (25775 - 25600) / (6500 - 6000) = 3.5

The vertical intercept for this graph is at the point (0, 200) and represents a cost of $200 when a quantity of 0 face masks are produced. The rate of change for C(a) is 3.5 and means the cost is increasing by $3.50 for every additional thousand face masks produced.

The linear equation for C(x) is C(x) = 3.5x + 200.

Based on this model, C(11) = 3.5(11) + 200 = 238.5, which means that when a quantity of 11,000 face masks are produced, there is a cost of $238.50.

Solving C(x) = 90,700 shows x = 25.5, which represents that for a cost of $90,700, you can produce 25,500 face masks.

The appropriate domain of this function is (0, INF) (interval notation- use INF for infinity if needed).