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?
a. C = 8x + 75.
b. C = 8x + 75 = 18,955
8x = 18,955 - 75 = 18,880
X = 2360.
c.
a. To write the cost equation, we are given that the fixed cost (b) is $75 and the marginal cost (m) is $8. Substituting these values into the equation C = mx + b, we have C = 8x + 75.
b. We are given that the total cost (C) in March was $18,955. To calculate the number of phones produced (x) using the equation, we can rearrange the equation as x = (C - b) / m. Substituting the given values, we have x = (18,955 - 75) / 8 = 18,880 / 8 = 2,360.
Therefore, the number of phones produced in March was 2,360.
c. To determine if the company met the goal of producing at least 2000 phones in March, we compare the number of phones produced (2,360) to the goal of 2000.
Mathematically, we can calculate the difference by subtracting the goal (2000) from the actual number of phones produced (2,360). If the result is positive, it means the company exceeded the goal. If the result is negative, it means the company missed the goal.
Difference = Number of phones produced - Goal = 2,360 - 2000 = 360
Since the difference is positive (360), it means the company exceeded the goal of producing at least 2000 phones in March.