Management analysts at a Fresno laboratory have developed the following LP primal problem:

Maximize profit = 23X1 + 18X2

Subject to 8X1 + 4X2 ≥ 0.5

4X1 + 6X2 ≥ 115

9X1 + 4X2 ≥ 116

This model represents a decision concerning number of hours spent by biochemists on certain laboratory experiments and number of hours spent by biophysicists on the same series of experiments (X2) A biochemist costs $23 per hour, while a biophysicist’s salary averages $18 per hour. Both types of scientists can be used on three needed laboratory operations: test 1, test 2, and test 3. The experiments and their times are shown in the accompanying table:

This means that a biophysicist can complete 8, 4, and 9 of tests 1, 2, and 3 per hour. Similarly, a biochemist can perform 4 of test 1, 6 of test 2, and 4 of test 3 per hour. The optimal solution to the lab’s primal problem is
X1 = 8.12 hours and X2 = 13.75 hours
Total cost = $434.37 per day
The optimal solution to the dual problem is
U1 = 2.07, U2 = 1.63, U3 = 0
(a) What is the dual of the primal LP problem?
(b) Interpret the meaning of the dual and itssolution.

Transcribed Image Text:

SCIENTIST TYPE MINIMUM TEST TIME NEEDED LAB EXPERIMENT BIOPHYSİCİST BIOCHEMIST PER DAY 120 115 116 Test 1 Test 2 Test 3 4 9