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 (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)

2 Jane sells jewellery. Her weekly commission is based on a sliding scale of \( 9 \% \) on the first \( \$ 2500 \) of her sales, \( 5 \% \) on the next \( \$ 5000 \) and \( 1 \% \) thereafter. She also gets a weekly retainer of \( \$ 500 \) Jane's weekly commission

laptop has a listed price of \( \$ 520.99 \) before tax. If the sales tax rate is \( 6.75 \% \), find the total cost of the laptop with sales tax included. ound your answer to the nearest cent, as necessary. \$ \( \square \)

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.)

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.)

camera has a listed price of \( \$ 779.98 \) before tax. If the sales tax rate is \( 9.75 \% \), find the total cost of the camera with sales tax included Round your answer to the nearest cent, as necessary. \$ \( \square \)