suppose that the dollar cost of producing x appliances is c(x)=1000+90x-0.2x2
a) find the average cost per appliance of producing the first 110 appliances.
b)find the marginal cost when 110 appliances are produced
c)show that the marginal cost when 110 appliances are produced is approximately the cost of producing one more appliance after the first 110 have been made, by calculating the latter cost directly.
a) find the average cost per appliance of producing the first 110 appliances.
b)find the marginal cost when 110 appliances are produced
c)show that the marginal cost when 110 appliances are produced is approximately the cost of producing one more appliance after the first 110 have been made, by calculating the latter cost directly.
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a) Total cost = 1000 + 90*110 - 110²/5 = $8480
Average cost = $8480 ÷ 110 = $77.09
b) Marginal cost = dc/dx = 90 - 2x/5
When x = 110, marginal cost = 90 - 44 = $46
c) Cost of producing 111 appliances = 1000 + 90*111 - 111²/5 = $8525.80
Cost of producing 110 appliances = 1000 + 90*110 - 110²/5 = $8480
Cost of producing the 111th appliance = $8525.80 - $8480 = $45.80
This is very close to the answer in part (b).
Average cost = $8480 ÷ 110 = $77.09
b) Marginal cost = dc/dx = 90 - 2x/5
When x = 110, marginal cost = 90 - 44 = $46
c) Cost of producing 111 appliances = 1000 + 90*111 - 111²/5 = $8525.80
Cost of producing 110 appliances = 1000 + 90*110 - 110²/5 = $8480
Cost of producing the 111th appliance = $8525.80 - $8480 = $45.80
This is very close to the answer in part (b).