8. Considere la situación de inventarios en la cual las existencias se reponen de manera unifor- me (en lugar de instantáneamente) a una tasa \( a \). El consumo ocurre a la tasa constante \( D \). Ya que el consumo también ocurre durante el periodo de reposición, es necesario que \( a>D \). El costo de preparación es \( K \) por pedido, y el costo de retención es \( h \) por unidad, por unidad de tiempo. Si \( y \) es el tamaño del pedido y no se permite que haya escasez, demuestre que (a) El nivel máximo del inventario es \( y\left(1-\frac{D}{a}\right) \). (b) El costo total por unidad de tiempo dado \( y \) es TCU(y) \( =\frac{K D}{y}+\frac{h}{2}\left(1-\frac{D}{a}\right) y \) WWW.FreeLibrOS.COM 13.3 Modelos estáticos de cantidad de pedido económico (EOQ) (c) La cantidad de pedido económica es (d) Demuestre que la EOQ en la situación de reposición instantánea puede derivarse de la fórmula en (c)

What is the approximate balance after 20 years? Choose the correct answer below. \( \begin{array}{ll}\text { A. } \$ 200 & \text { B. } \$ 400 \\ \text { C. } \$ 100 & \text { D. } \$ 10 \\ \text { b) About how fast is the balance increasing after } 20 \text { years? } \\ \text { Choose the correct answer below. } \\ \begin{array}{ll}\text { A. } \$ 5 / y e a r & \text { B. } \$ 200 / y e a r \\ \text { C. } \$ 20 / y e a r & \\ \text { c) Use the answers to parts a) and b) to determine the interest rate. }\end{array} \\ \text { The interest rate is } \square \% .\end{array} \)

A farm purchased in 2000 for \( \$ 1 \) million was valued at \( \$ 3 \) million in 2008. If the farm continues to appreciate at the same rate (with continuous compounding), when will it be worth \( \$ 14 \) million? Find a function \( \mathrm{A}(\mathrm{t}) \) that gives the current value of the farm. \( \mathrm{A}(\mathrm{t})=\square \) (Type an exact answer.)

Find the present value of \( \$ 7,000 \) to be received in 5 years, if money may be invested at \( 7.2 \% \) with interest compounded continuously. The present value is \( \$ \square \). (Round to the nearest cent as needed.)

How much money must you invest now at \( 4.2 \% \) interest compounded continuously in order to have \( \$ 10,000 \) at the end of 4 years? You must invest \( \$ \square \). (Round to the nearest cent as needed.)

A man invests his savings in two accounts, one paying 6 percent and the other paying 10 percent simple interest per year. He puts twice as much in the lower-yielding account because it is less risky. His annual interest is 8250 dollars. How much did he invest at each rate? Your answer is total in the account paying 6 percent interest is total in the account paying 10 percent interest is