Optimization

The process that solves for the best possible outcome

Optimization Questions

• Optimizing Product and Sum
• Optimizing Set Surface Area Find Volume
• Optimizing Box Corner Cut
• Optimizing Nearest Point
• Optimizing Boat Distance
• Optimizing Manufacturing Amounts
• Optimizing Rebates
• Optimizing Box Cost
• Optimizing Pen Profit
• Optimizing Cable Length
• Optimizing Rectangle In Semicircle

Optimizing In Economics

Extreme Problems In Economics

• $C(x)\to$ Cost function
  • $C^{\prime }(x)\to$ Marginal Cost
• $c(x)\to$ average cost
  • $c(x)=\frac{C(x)}{x}$
• $p(x)\to$ Demand/Price Function
• $R(x)\to$ Revenue Function
  • $R(x)=xp(x)$
  • $R^{\prime }(x)\to$ Marginal Revenue Function
• $P(x)\to$ Profit Function
  • $P(x)=R(x)-C(x)$
  • $P^{\prime }(x)\to$ Marginal Profit

Average cost is a minimum when marginal cost = average cost * when the average rate of change = instantaneous rate of change