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The cost can be optimized by using a Linear Programming given the linear constraint system
- To minimize the cost, the biologist should use <u>60 samples of Type I</u> bacteria and <u>0 samples of Type II</u> bacteria
Reason:
Let <em>X</em> represent Type 1 bacteria, and let <em>Y</em>, represent Type II bacteria, we have;
The constraints are;
4·X + 3·Y ≥ 240
20 ≤ X ≤ 60
Y ≤ 70
P = 5·X + 7·Y
Solving the inequality gives;
4·X + 3·Y ≥ 240
(Equation for the inequality graphs)
The boundary of the feasible region are;
(20, 70)
(20, 53.)
(60, 0)
(60, 70)
The cost are ;
- Therefore, the minimum cost of $300 is obtained by using <u>60 samples of Type I</u> and <u>0 samples of Type II</u>
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