Linear programming: A biologist needs at least 40 fish for

[xMakubex]

I am having a lot of trouble with the following linear programming assignment:

8. A biologist needs at least 40 fish for her experiment. she cannot use more than 25 perch or more than 30 bass. Each perch cost $5, and each bass $3. How many of each fish should she use in order to minimize cost?

1. Identify your variables:

. . .x: perch
. . .y: bass
. . .?

2. Identify all constraints using above variables

3. Identify objective function

4. Graph constraints on full page of graph paper to find feasible region

5. Identify vertices of feasible region

6. Find vertex that produces maximum (or minimum) using objective function

7. Write conclusion for problem.

I have no idea what to do!! please help!

 

[galactus]

x=perch
y=bass

She needs at least 40 fish: \(\displaystyle x+y\geq40\)

The perch are $5 each, but no more than 25 of them:

Cost = \(\displaystyle 5x\leq125\)

The bass are $3 each, but no more than 30 of them:

Cost = \(\displaystyle 3y\leq90\)