The cost of producing cell phones is represented as C=mx+b, where m is the marginal cost, x is the number of phones produced, b is the fixed cost, and C is the final cost.
a. If the fixed cost is $75 and the marginal cost is $8, write the cost equation.
b. In March, the total cost was $18,955. Calculate the number of phones produced using the equation.
c. If the goal for March was to produce at least 2000 phones, did the company meet this goal? Show mathematically the number of phones exceeded or missed the goal?
Thank you for the help!!!
c = m x + b
c = 8 x + 75
18955 = 8 x + 75
x = 2360
2360 - 2000 = 360 in excess of 2000 goal
a. To write the cost equation, we need to substitute the given values into the equation C = mx + b. Given that the fixed cost (b) is $75 and the marginal cost (m) is $8, we substitute these values to get: C = 8x + 75.
b. To calculate the number of phones produced using the equation, we need to substitute the given total cost (C) of $18,955 into the equation C = 8x + 75 and solve for x. Setting C equal to 18,955, the equation becomes:
18,955 = 8x + 75
Subtracting 75 from both sides:
18,880 = 8x
Dividing both sides by 8:
x = 18,880 / 8
x ≈ 2,360
So, approximately 2,360 phones were produced in March.
c. To determine if the company met the goal of producing at least 2000 phones in March, we need to compare the number of phones produced (x) to the goal (2000).
The company produced approximately 2,360 phones, so let's compare this to the goal:
Number of phones produced (x) = 2,360
Goal = 2,000
The number of phones produced (x) is greater than the goal (2,000):
2,360 > 2,000
Hence, the company met and exceeded the goal of producing at least 2000 phones.