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. To write the cost equation, we can substitute the given values of the fixed cost (b) and the marginal cost (m) into the equation C = mx + b.
Given that the fixed cost is $75 and the marginal cost is $8, the cost equation becomes:
C = 8x + 75
b. To calculate the number of phones produced in March, we need to solve the given cost equation for x when the total cost (C) is $18,955.
Substituting C = 18,955 into the cost equation, we have:
18,955 = 8x + 75
To isolate the variable x, we can subtract 75 from both sides of the equation:
18,955 - 75 = 8x
18,880 = 8x
Finally, to solve for x, we divide both sides of the equation by 8:
x = 18,880 / 8
x = 2,360
Therefore, the number of phones produced in March is 2,360.
c. To determine if the company met the goal of producing at least 2000 phones in March, we compare the actual production value (2,360 phones) with the goal (2000 phones).
If the number of phones produced (x) is greater than or equal to the goal (2000), then the company met the goal. Otherwise, it missed the goal.
Mathematically, we can write this as:
x ≥ 2000
Plugging in the value of x as 2,360, we have:
2,360 ≥ 2000
Since 2,360 is indeed greater than 2000, we can conclude that the company met the goal of producing at least 2000 phones in March.