$13-20$ Refer to Problem $13\mathrm{.}19.$ Suppose the sale of football programs described by the probability distribution in that problem applies only to days when the weather is good. When poor weather occurs on the day of a football game, the crowd that attends the game is only half of capacity. When this occurs, the sales of programs decreases, and the total sales are given in the following table:

$\backslash$table$[[$NUMBER $($IN $100$S$)$ OF PROGRAMS SOLD,PROBABILITY$],[12,0\mathrm{.}25],[13,0\mathrm{.}24],[14,0\mathrm{.}19],[15,0\mathrm{.}17],[16,0\mathrm{.}15]]$

Programs must be printed $2$ days prior to game day. The university is trying to establish a policy for determining the number of programs to print based on the weather forecast.

a$.$ If the forecast is for a $20\%$ chance of bad weather, simulate the weather for $10$ games with this forecast. Use column $4$ of Table $13\mathrm{.}4[.$

b$.$ Simulate the demand for programs at $10$ games in which the weather is bad. Use column $5$ of the random number table $($Table $13\mathrm{.}4.$ and begin with the first number in the column.

c$.$ Beginning with a $20\%$ chance of bad weather and an $80\%$ chance of good weather, develop a flowchart that would be used to prepare a simulation of the demand for football programs for $10$ games.

d$.$ Suppose there is a $20\%$ chance of bad weather and the university has decided to print $2,500$ programs. Simulate the total profits that would be achieved for $10$ football games.