MATH 101, 250 Algebra_Piecewise Defined Functions, Modeling, Domain/Range

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Piecewise Defined Functions, Modeling, Domain/Range 1. Factory in Wichita

A) The cost of producing 25,000 units is $1. From 25,001 units to 35,000 units the cost

lowers to $0.80.

B) f(x)= {$1, for 1 \< x < 25,000 $0.80, for 25,000, x < 35,000 C) The cost is $0.80 D) The company should calculate the marginal cost and make adjustments E) ___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.

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2. Factory in Seattle

A) B) When x <= 8000 The cost remains constant at 0.35 when x increases from 0 to

8000 The slope of cost function over this part is 0. When 8000 < x <= 20000 The cost remains constant at 0.75 when x increases from 8000 to 20000 The slope of cost function over this part is 0. When 20000 < x <= 42000 The cost decreases when x increases from 20000 to 42000 The slope of cost function

3. Factory in Omaha A) The rate of decrease is 0.00001 dollars per unit B) The function will then be y = -0.00001x + 0.97 C) The cost per unit at the production level of 19,000 is 0.78 dollars

4. Analysis and Making Production Decisions A) Wichita: $1 Seattle: $0.75 B) We will send the order to the Seattle factory since they have the lowest cost per unit.

B2) Combination A Wichita: 7,000 units = $1 Seattle: 30,000 units = $0.68 Average Cost: $0.74

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Combination B Wichita: 7,000 units = $1 Omaha: 30,000 units = $0.67 Average Cost: $0.73

Combination C Seattle: 7,000 units = $0.35 Omaha: 30,000 units = $0.67 Average Cost: $0.61

Combination D Omaha: 7,000 units = $0.85 Seattle: 30,000 units = $0.68 Average Cost: $0.71

Combination E Omaha: 7,000 units = $0.85 Wichita: 30,000 units = $0.80 Average Cost: $0.81

Combination F Seattle: 7,000 units = $0.35 Wichita: 30,000 units = $0.80 Average Cost: $0.71 B3) Orders B and C should be produced by Omaha's factory.

Total # of units produced for the company today: 37,000 Average cost per unit for all production today: $0.60

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