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iannic2
 3 years ago
A company makes two products, widgets and gadgets, which use the same materials in their production. Given a fixed amount of materials and labor, the company must decide how many widgets and gadgets to produce. If w widgets and g gadgets are produced w and g must satisfy 9w^2+4g^2=18000. The graph of this equation for w>=0 g>=0 is called production possibilities curve, and a point (w,g) on this curve is a production scheduel for the company. If a widget gives a profit of 3 dollars and a gadget gives a profit of 4 dollars, find the production schedule that maximizes profit, using lagrange m
iannic2
 3 years ago
A company makes two products, widgets and gadgets, which use the same materials in their production. Given a fixed amount of materials and labor, the company must decide how many widgets and gadgets to produce. If w widgets and g gadgets are produced w and g must satisfy 9w^2+4g^2=18000. The graph of this equation for w>=0 g>=0 is called production possibilities curve, and a point (w,g) on this curve is a production scheduel for the company. If a widget gives a profit of 3 dollars and a gadget gives a profit of 4 dollars, find the production schedule that maximizes profit, using lagrange m

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shaan_iitk
 3 years ago
Best ResponseYou've already chosen the best response.1okk ... see my profit is 3w + 4g ... and my condition is (3w)^2 + (2g)^2  18000 apply langrange we get w and g in terms of the constant \[\lambda\] = x w = 3/(18x) and g = 4/(8x) .. place these two values in the consition to get x = 1/(120) hence w = 20 and g = 60 and hence my profit is = 60 + 240 = 300
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