Set up the initial simplex tableau that could be used to solve the following problem by the simplex method.
The Fancy Fashions, an independent, local boutique, has $8000 available each month for advertising. Newspaper ads cost $500 each, and no more than 40 can run per month. Internet banner ads cost $25 each, and no more than 60 can run per month. TV ads cost $2000 each, with a maximum of 10 available each month. Approximately 5000 women will see each newspaper ad, 3000 will see each Internet banner, and 12,000 will see each TV ad. How much of each type of advertising should be used if the store wants to maximize its ad exposure?
Let $x_1$ = the number of newspaper ads. Let $x_2$ = the number of Internet banner ads. Let $x_3$ = the number of TV ads. Complete the initial simplex tableau below.
$$
\begin{array}{cccccccc}
x_1 & x_2 & x_3 & s_1 & s_2 & s_3 & s_4 & z \\
500 & \Box & \Box & 1 & \Box & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & \Box & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & \Box & 1 & 0 & 0 \\
0 & 0 & 1 & 0 & \Box & 0 & 1 & 0 \\
\hline
\Box & \Box & \Box & 0 & 0 & 0 & 0 & 1
\end{array}
$$
