a. In order to determine whether or not there is a significant difference between the hourly wages of two companies, a random sample of 15 employees from Company 1 and another random sample of 13 employees from Company 2 were selected. The following sample data were observed.

	Company 1	Company 2
Mean	$18.9	$17.7
Standard deviation	$2.1	$1.9

i. Do the data indicate that there is a significant difference between the hourly wages of two companies at significance level of 0.05? Assume that population variances are equal. What conclusion can you make?

ii. Based on the test result, which type of decision error may have occurred? Explain.

b. You are trying to decide how many vitamin pills to take. SuperV brand vitamin pills each contain 3 mg of vitamin A, 2 mg of vitamin B, and 1 mg of vitamin C. Topper brand vitamin pills each contain 2 mg of vitamin A, 1 mg of vitamin B and 3 mg of vitamin C. You want to take enough pills daily to get at least 18 mg of vitamin A, 14 mg of vitamin B and 20 mg of vitamin C. However, SuperV pills cost 7 cents each and Toppers cost 5 cents each, and you would like to minimize the total cost of your daily dosage. Formulate the problem as a linear programming model.