**Enter answers using TWO decimal places A student project at WCU was initiated
ID: 3142992 • Letter: #
Question
**Enter answers using TWO decimal places
A student project at WCU was initiated to try to determine the impact of implementation of new technologies. The students want to survey both distance and residential undergraduate students in the four different years at Western (first year, sophomore, junior, and senior). They have estimated that it will cost them $5.50 to survey first year and sophomore residential students and $8.00 to survey junior and senior residential students. The cost to interview distance students is slightly higher. It will cost $6.75 for first year and sophomores and $9.50 for junior and seniors. For statistical validity they want to interview at least 900 students. They feel that there are certain criteria that they must adhere to: At least 25% of first year students surveyed should be distance students At least 20% of sophomore students surveyed should be distance students At least 35% of junior students surveyed should be distance students At least 40% of senior students surveyed should be distance students No more than 35% of all the students surveyed should be first year students Juniors and seniors should be at least 45% of the students surveyed Each of the eight types of students must be represented in the survey by at least 10% of the total interviews Formulate and solve this problem in Excel to determine the number of each type of student that should be surveyed that meets the requirements and minimizes the cost to carry out the interviews. a) What is the minimum cost in your optimal solution (the value of the objective function)? b) If the cost of surveying first year and sophomore residential students increases from $5.50 to $7.00- What is the minimum cost in your optimal solution?Explanation / Answer
MINIMUM INTERVIEW COST
SOLUTION TO PART A STUDENTS CATEGORY INTERVIEW NO OF STUDENTS COST $ TO BE INTERVIEWED DISTANCE FIRST YEAR 6.75 90 RESIDENTIAL FIRST YEAR 5.50 225 DISTANCE SOPHOMORE 6.75 90 RESIDENTIAL SOPHOMORE 5.50 90 DISTANCE JUNIOR 9.50 90 RESIDENTIAL JUNIOR 8.00 135 DISTANCE SENIOR 9.50 90 RESIDENTIAL SENIOR 8.00 90 TOTAL STUDENTS 900 CONSTRAINTS REFERENCE CELLS TOTAL FIRST YEAR STUDENTS 315 TOTAL JUNIOR & SENIOR STUDENTS 405 TOTAL INTERVIEWS EQUALS 900 DISTANCE FIRST YEAR H3 GREATERTHAN OR EQUAL TO 78.75 DISTANCE SOPHOMORE H5 GREATERTHAN OR EQUAL TO 36.00 DISTANCE JUNIOR H7 GREATERTHAN OR EQUAL TO 78.75 DISTANCE SENIOR H9 GREATERTHAN OR EQUAL TO 63.00 FIRST YEAR STUDENTS (H3+H4) H13 LESSTHAN OR EQUAL TO 315.00 JUNIORS & SENIORS H14 MORETHAN OR EQUAL TO 405.00 EACH CATEGORY H3,H4,H5,H6,H7,H8,H9,H10 MORETHAN OR EQUAL TO 90.00 OBJECTIVE FUNCTION SUMPRODUCT(F3:F10,H3:H10) 6457.5MINIMUM INTERVIEW COST
SOLUTION TO PART B STUDENTS CATEGORY INTERVIEW NO OF STUDENTS COST $ TO BE INTERVIEWED DISTANCE FIRST YEAR 6.75 225 RESIDENTIAL FIRST YEAR 7.00 90 DISTANCE SOPHOMORE 6.75 90 RESIDENTIAL SOPHOMORE 7.00 90 DISTANCE JUNIOR 9.50 90 RESIDENTIAL JUNIOR 8.00 135 DISTANCE SENIOR 9.50 90 RESIDENTIAL SENIOR 8.00 90 TOTAL STUDENTS 900 CONSTRAINTS REFERENCE CELLS TOTAL FIRST YEAR STUDENTS 315 TOTAL JUNIOR & SENIOR STUDENTS 405 TOTAL INTERVIEWS EQUALS 900.00 DISTANCE FIRST YEAR H3 GREATERTHAN OR EQUAL TO 78.75 DISTANCE SOPHOMORE H5 GREATERTHAN OR EQUAL TO 36.00 DISTANCE JUNIOR H7 GREATERTHAN OR EQUAL TO 78.75 DISTANCE SENIOR H9 GREATERTHAN OR EQUAL TO 63.00 FIRST YEAR STUDENTS (H3+H4) H13 LESSTHAN OR EQUAL TO 315.00 JUNIORS & SENIORS H14 MORETHAN OR EQUAL TO 405.00 EACH CATEGORY H3,H4,H5,H6,H7,H8,H9,H10 MORETHAN OR EQUAL TO 90.00 OBJECTIVE FUNCTION SUMPRODUCT(F3:F10,H3:H10) 6896.25 MINIMUM INTERVIEW COSTRelated Questions
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