The cost C of producing x thousand calculators is given by the following equation.
C=-15.2x^2+15,990x+580,000(x≤175)
Find the average cost per calculator for each of the following production levels.
40,000; 60,000 and 175,000
for each part, just divide the total cost by how many calculators:
C(x)/x
To find the average cost per calculator, you need to divide the cost by the number of calculators produced.
1. For a production level of 40,000 calculators:
C = -15.2x^2 + 15,990x + 580,000 (where x ≤ 175)
C = -15.2(40)^2 + 15,990(40) + 580,000
C = -15.2(1600) + 639,600 + 580,000
C = -24,320 + 639,600 + 580,000
C = 1,195,280
Average cost per calculator = C / x
Average cost per calculator = 1,195,280 / 40,000
Average cost per calculator = 29.88 dollars
Therefore, the average cost per calculator for a production level of 40,000 calculators is $29.88.
2. For a production level of 60,000 calculators:
C = -15.2x^2 + 15,990x + 580,000 (where x ≤ 175)
C = -15.2(60)^2 + 15,990(60) + 580,000
C = -15.2(3600) + 959,400 + 580,000
C = -54,720 + 959,400 + 580,000
C = 1,484,680
Average cost per calculator = C / x
Average cost per calculator = 1,484,680 / 60,000
Average cost per calculator = 24.74 dollars
Therefore, the average cost per calculator for a production level of 60,000 calculators is $24.74.
3. For a production level of 175,000 calculators:
C = -15.2x^2 + 15,990x + 580,000 (where x ≤ 175)
C = -15.2(175)^2 + 15,990(175) + 580,000
C = -15.2(30,625) + 2,780,250 + 580,000
C = -465,500 + 2,780,250 + 580,000
C = 2,894,750
Average cost per calculator = C / x
Average cost per calculator = 2,894,750 / 175,000
Average cost per calculator = 16.54 dollars
Therefore, the average cost per calculator for a production level of 175,000 calculators is $16.54.
To find the average cost per calculator for each of the given production levels, we need to divide the cost by the number of calculators produced.
Let's start by finding the cost for each production level:
1. For 40,000 calculators:
To find the cost, we substitute x = 40 into the equation:
C = -15.2(40)^2 + 15,990(40) + 580,000
Calculate the value of C.
2. For 60,000 calculators:
To find the cost, we substitute x = 60 into the equation:
C = -15.2(60)^2 + 15,990(60) + 580,000
Calculate the value of C.
3. For 175,000 calculators:
The given equation only applies when x ≤ 175. So, when producing 175,000 calculators, the equation changes to:
C = 580,000
No calculation is needed in this case.
After finding the cost for each production level, we can calculate the average cost per calculator by dividing the cost by the number of calculators produced.
For example, for the given level of 40,000 calculators, the average cost per calculator would be the cost for 40,000 calculators divided by 40,000.
Repeat the same process for the other production levels: 60,000 calculators and 175,000 calculators.
Remember to perform all the necessary calculations and substitute the values into the equation to obtain the final answers.