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?
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a. To write the cost equation, we substitute the given values into the equation C = mx + b:
C = (m) * (x) + b
Given that the fixed cost is $75 and the marginal cost is $8, we substitute these values into the equation:
C = (8) * (x) + 75
Therefore, the cost equation is C = 8x + 75.
b. To calculate the number of phones produced in March, we use the cost equation and substitute the given total cost of $18,955:
18,955 = 8x + 75
To solve for x, we need to isolate the variable. Subtracting 75 from both sides of the equation gives us:
18,955 - 75 = 8x
Combining like terms simplifies the equation:
18,880 = 8x
To isolate the variable x, we divide both sides of the equation by 8:
x = 18,880 / 8
Evaluating the division gives us:
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 number of phones produced (2,360) with the goal (2000).
Mathematically, we can show whether the goal was exceeded or missed by comparing the two values:
Number of phones produced (2,360) - Goal (2000)
2,360 - 2000 = 360
The resulting value of 360 indicates that the number of phones produced exceeded the goal by 360 phones.