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A certain company manufactures and sells golf carts. At the end of each week, the company transfers the carts produced that week into storage (inventory). All carts that are sold are taken from the inventory. A simple model of this process is

I(k+1)=P(k)+I(k)S(k)I ( k + 1 ) = P ( k ) + I ( k ) - S ( k )

where

P(k)= number of carts produced in week kI(k)= number of carts in inventory in week kS(k)= number of carts sold in week k\begin{array} { l } { P ( k ) = \text { number of carts produced in week } k } \\ { I ( k ) = \text { number of carts in inventory in week } k } \\ { S ( k ) = \text { number of carts sold in week } k } \end{array}

The projected weekly sales for 10 weeks are

Week12345678910Sales50556070707580809055\begin{matrix} \text{Week} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8} & \text{9} & \text{10}\\ \text{Sales} & \text{50} & \text{55} & \text{60} & \text{70} & \text{70} & \text{75} & \text{80} & \text{80} & \text{90} & \text{55}\\ \end{matrix}

Suppose the weekly production is based on the previous week's sales so that P(k)=S(k1)P ( k ) = S ( k - 1 ) . Assume that the rst week's production is 50 carts; that is, P(1)=50.P ( 1 ) = 50 . Write a MATLAB program to compute and plot the number of carts in inventory for each of the 10 weeks or until the inventory drops below zero. Run the program for two cases: (a) an initial inventory of 50 carts so that I(1)=50I(1)=50 and (b) an initial inventory of 30 carts so that I(1)=30I(1)=30.

Question

septem Aegyptii me circumveniebant. duos graviter vulneravi, sed ceteri me superaverunt. procubui exanimatus. Seven Egyptians were surrounding me. I wounded two of them gravely, but the rest overcame me. I fell to the ground, unconscious. Quintus fought bravely, but he was outnumbered. He only managed to fight off two of the attackers before he was wounded himself.

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