Lets consider a simplified analysis of Burger Kings situation. Consider a region with 180 restaurants served by a single distribution center. At the time the order must be placed with the factories in Asia, demand (units of toys) for the promotion at each restaurant is forecasted to be gamma distributed with mean 2,242 and standard deviation 1,900. A discrete version of that gamma distribution is provided in the following table, along with a graph of the density function:

Suppose six months in advance of the promotion, Burger King must make a single order for each restaurant. Furthermore, Burger King wants to have an in-stock probability of at least 85 percent. Q1. Given those requirements, how many toys must each restaurant order? (Round your answer to the nearest whole number.) Q2. How many toys should Burger King expect to have at the end of the promotion? (Round your answer to the nearest whole number.)

\begin{tabular}{rcr} \multicolumn{1}{c}{Q} & F(Q) & \multicolumn{1}{c}{I(Q)} \\ 0 & 0.0000 & 0 \\ 500 & 0.1312 & 0 \\ 1,000 & 0.3101 & 65.6 \\ 1,500 & 0.4728 & 220.6 \\ 2,000 & 0.6062 & 457.0 \\ 2,500 & 0.7104 & 760.1 \\ 3,000 & 0.7893 & 1,115.3 \\ 3,500 & 0.8480 & 1,510.0 \\ 4,000 & 0.8911 & 1,934.0 \\ 4,500 & 0.9224 & 2,379.5 \\ 5,000 & 0.9449 & 2,840.7 \\ 5,500 & 0.9611 & 3,313.2 \\ 6,000 & 0.9726 & 3,793.7 \\ 6,500 & 0.9807 & 4,280.0 \\ 7,000 & 0.9865 & 4,770.4 \\ 7,500 & 0.9906 & 5,263.6 \\ 8,000 & 0.9934 & 5,758.9 \\ 8,500 & 0.9954 & 6,255.6 \\ 9,000 & 0.9968 & 6,753.3 \\ 9,500 & 0.9978 & 7,251.7 \\ 10,000 & 0.9985 & 7,750.6 \\ 10,500 & 0.9989 & 8,249.8 \\ 11,000 & 0.9993 & 8,749.3 \\ 11,500 & 0.9995 & 9,248.9 \\ 12,000 & 1.0000 & 9,748.7 \end{tabular}