The number of bottles of each brand that is added to satisfy the needs of the reef tank at the minimum possible cost.
Answer to Problem 39E
The minimum cost is $125 and this occurs when 2 bottle of brand X and 5 bottles of brand Y are added.
Explanation of Solution
Given information:
The public aquarium is adding coral nutrients to large reef tank. The minimum amount of nutrients A, B, and C that need to be added to the tank are 30 units, 16 units, 24 units.
Formula used:
x be the number or bottles of brand X and y be the number of bottles of brand Y.
Calculation:
Let x be the number or bottles of brand X and y be the number of bottles of brand Y.
Consider the constraints,
The cost C is given by
We have to determine the minimum cost.
The below graph shows the feasible region.
Now, evaluate the objective function at the comer point to find the minimum value.
At
Hence, the minimum cost is $125 and this occurs when 2 bottle of brand X and 5 bottles of brand Y are added.
Conclusion:
The minimum cost is $125 and this occurs when 2 bottle of brand X and 5 bottles of brand Y are added.
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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