Final answer:
The total cost of producing 9 mirrors is $456. The marginal cost of producing the 8th mirror is $60. The average cost of producing 4 mirrors is $49 per mirror, and the marginal average cost of producing the 7th mirror is approximately $0.86.
Step-by-step explanation:
The total cost of producing mirrors using the function C(x)=132+4x2 can be calculated by substituting 'x' with the number of mirrors to be produced. To find the total cost of producing 9 mirrors, we substitute 'x' with 9:
C(9)=132+4(9)2=132+4(81)=132+324=456. So, the total cost of producing 9 mirrors is $456.
The marginal cost of producing the 8th mirror is the additional cost of producing one more unit after the 7th. This requires calculating the cost for 7 mirrors and 8 mirrors and then finding the difference:
C(8)=132+4(8)2=132+4(64)=132+256=388
C(7)=132+4(7)2=132+4(49)=132+196=328
The marginal cost of the 8th mirror is then $388-$328=$60.
To find the average cost of producing 4 mirrors, we calculate C(4) and then divide by the quantity (4):
C(4)=132+4(4)2=132+4(16)=132+64=196
The average cost for 4 mirrors is then $196/4=$49 per mirror.
The marginal average cost of producing the 7th mirror is the difference between the average cost for 7 mirrors and the average cost for 6 mirrors:
Average cost for 7 mirrors: C(7)/7 = $328/7 ≈ $46.86
Average cost for 6 mirrors: C(6)/6 = (132+4(6)2)/6 = (132+4(36))/6 = (132+144)/6 = 276/6 = $46
The marginal average cost of the 7th mirror is then ≈ $46.86 - $46 = $0.86.