The total cost​ (in dollars) of manufacturing x auto body frames is ​C(x)=60,000+400x. ​(A) Find the average cost per unit if 200 frames are produced. ​(B) Find the marginal average cost at a production level of 200 units. ​(C) Use the results from parts​ (A) and​ (B) to estimate the average cost per frame if 201 frames are produced.

Answer:

a) Average price per unit = 700

b) average marginal cost = -1.5 dollars/frame

c) For 201 frames are produced = $698.5

Explanation:

Given Data:

C(x) = 60000 + 400x

a) Average cost for 200 units:

Total Cost of 200 units will be:

C(200) = 60000 + 400(200)

C(200) = 140,000

Total Cost of 200 units = 140,000

Average price per unit = Total Cost / number of units

Average price per unit = 140,000/200

Average price per unit = 700

b) Marginal Average Cost:

We know that marginal cost = [tex]C^{'}[/tex](x)

And the average marginal cost = [tex]\frac{d}{dx}[/tex] [tex]\frac{C(x)}{x}[/tex]

So,

= the derivative of ([tex]\frac{60,000 + 400(x)}{x}[/tex])

= the derivative of ([tex]\frac{(60,000)}{x} + 400[/tex])

= [tex]\frac{-60,000}{x^{2} }[/tex] + 0

So,

average marginal cost = [tex]\frac{-60,000}{x^{2} }[/tex]

at x = 200 units

average marginal cost = [tex]\frac{-60,000}{200^{2} }[/tex]

average marginal cost = -1.5 dollars/frame

c) Average cost per frame if 201 frames are produced:

We already seen in the part b that, the average marginal cost is decreasing by 1.5 dollars /frame. So,

if 201 frames are produced the instead of 200 then the difference is of 1 frame and we discussed that average marginal cost of 1 frame is decreasing at 1.5 dollars per frame.

So,

As we know the average cost from part a = 700 dollars.

Therefore, for 201 item = 700 dollars -1.5 dollars

For 201 frames are produced = $698.5

OHARA COMPANY
Income Statement
For the Year Ended December 31, 2017
Net sales $2,218,500
Cost of goods sold 1,012,400
Selling and administrative expenses 906,000
Interest expense 78,000
Income tax expense 69,000
Net income $ 153,100
OHARA COMPANY
Balance Sheet
December 31, 2017
Assets
Current assets
Cash $ 60,100
Debt investments 84,000
Accounts receivable (net) 169,800
Inventory 145,000
Total current assets 458,900
Plant assets (net) 575,300
Total assets $ 1,034,200
Liabilities and Stockholders’ Equity
Current liabilities
Accounts payable $ 160,000
Income taxes payable 35,500
Total current liabilities 195,500
Bonds payable 200,000
Total liabilities 395,500
Stockholders’ equity
Common stock 350,000
Retained earnings 288,700
Total stockholders’ equity 638,700
Total liabilities and stockholders’ equity
$1,034,200



Additional information: The net cash provided by operating activities for 2017 was $190,800. The cash used for capital expenditures was $92,000. The cash used for dividends was $31,000. The weighted-average number of shares outstanding during the year was 50,000.

(i) Working capital. (2016: $160,500; 2017: $263,400)
(ii) Current ratio. (2016: 1.65:1; 2017: 2.35:1)
(iii) Free cash flow. (2016: $48,700; 2017: 67,800)
(iv) Debt to assets ratio. (2016: 31%; 2017: 38.2%)
(v) Earnings per share. (2016: $3.15; 2017: $3.06)

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