By George Abbott Osborne
Excerpt from Examples of Differential Equations: With principles for his or her Solution
Many of the examples were accumulated from ordinary treatises, yet a substantial quantity were ready by means of the writer to demonstrate designated problems, or to professional vide routines corresponding extra approximately with the talents of general scholars. With few exceptions they've got all been validated by way of use within the class-room.
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Extra info for Examples of Differential Equations Osborne
00. 00 of revenue. But the vertex (kink point) at 3 1/3, 3 1/3 is better for it yields revenue of 6 2/3. 5. Each iso-revenue curve constitutes the locus of all points yielding the same revenue. 00 iso-revenue curve are feasible. Point 3 1/3, 3 1/3 is feasible and lies on the 6 2/3 iso-revenue curve. Since the 6 2/3 iso-revenue curve just touches the production transformation curve only at point 3 1/3, 3 1/3 , graphical intuition suggests that this point yields the revenue maximizing output. 10 To determine the kink-point note that it must lie on both 2X + 4Y = 20 and 2X + Y = 10.
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2 Production transformation — Mobilizing for World War II For a second production transformation curve example, consider the mobilization of the United States economy for World War II. 2 is a rough but not unreasonable estimate of the tradeoﬀs between producing civilian goods versus production for the war eﬀort. On the ordinate (y-axis) we plot total expenditures on war. On the abscissa (x-axis) we have civilian utilization, deﬁned as Gross Domestic Product minus wartime expenditure. 3 In 1939 we had civilian utilization of 891 billion and war output of 12 billion.