Question

a company has an opportunity to bid on three contracts. determine which would be the best investment given the information in the table. probability of profit and loss by contract southeast: profit, probability of profit $45,000, 50\\%$; probability to break even $30\\%$; loss, probability of loss $6,000, 20\\%$ southwest: profit, probability of profit $60,000, 35\\%$; probability to break even $40\\%$; loss, probability of loss $10,000, 25\\%$ california: profit, probability of profit $112,000, 20\\%$; probability to break even $40\\%$; loss, probability of loss $40,000, 40\\%$

Explanation:

Step1: Calculate the expected value for Southeast

The expected value formula is \(E = x_1P_1 + x_2P_2+x_3P_3\). For Southeast, \(x_1 = 45000\), \(P_1=0.5\); \(x_2 = 0\) (break - even), \(P_2 = 0.3\); \(x_3=-6000\), \(P_3 = 0.2\).

$$E_{Southeast}=45000\times0.5+0\times0.3+( - 6000)\times0.2$$

$$E_{Southeast}=22500 - 1200=21300$$

Step2: Calculate the expected value for Southwest

For Southwest, \(x_1 = 60000\), \(P_1 = 0.35\); \(x_2 = 0\) (break - even), \(P_2=0.4\); \(x_3=-10000\), \(P_3 = 0.25\)

$$E_{Southwest}=60000\times0.35+0\times0.4+( - 10000)\times0.25$$

$$E_{Southwest}=21000-2500 = 18500$$

Step3: Calculate the expected value for California

For California, \(x_1 = 112000\), \(P_1=0.2\); \(x_2 = 0\) (break - even), \(P_2 = 0.4\); \(x_3=-40000\), \(P_3=0.4\)

$$E_{California}=112000\times0.2+0\times0.4+( - 40000)\times0.4$$

$$E_{California}=22400-16000=6400$$

Answer:

Southeast