Suppose you are running a factory, producing anvils that requires steel as a raw material. Your costs are predominantly human labor ($h$), which is $20 per hour for your workers, and the steel itself ($s$), which runs for $160 per ton. Suppose your revenue is loosely modeled by the following equation: $100h^{\frac{2}{3}}s^{\frac{1}{3}}$. If your budget is $10,000, how would you maximize revenue? Solve this problem using the Lagrangian method.

          Suppose you are running a factory, producing anvils that requires steel as a raw material.
Your costs are predominantly human labor ($h$), which is $20 per hour for your workers, and
the steel itself ($s$), which runs for $160 per ton. Suppose your revenue is loosely modeled
by the following equation: $100h^{\frac{2}{3}}s^{\frac{1}{3}}$. If your budget is $10,000, how would you maximize
revenue? Solve this problem using the Lagrangian method.

Suppose you are running a factory, producing anvils that requires steel as a raw material.
Your costs are predominantly human labor (h), which is 20 per hour for your workers, and
the steel itself (s), which runs for160 per ton. Suppose your revenue is loosely modeled
by the following equation: 100h^(2)/(3)s^(1)/(3). If your budget is 10,000, how would you maximize
revenue? Solve this problem using the Lagrangian method.

Added by Jack T.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Roee Shalom

Step 1

The objective function is the revenue, which is given by the equation 100hs. The constraint equation is the budget constraint, which is given by the equation 20h + 160s = 10,000. Show more…

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Totally lost on how to use the Lagrangian method. Please solve using all steps and show all work, while clearly explaining what you're doing, so I can learn. Thank you. Suppose you are running a factory producing anvils that requires steel as a raw material. Your costs are predominantly human labor (h), which is $20 per hour for your workers, and the steel itself (s), which runs for $160 per ton. Suppose your revenue is loosely modeled by the following equation: 100hs. If your budget is $10,000, how would you maximize revenue? Solve this problem using the Lagrangian method.