A chemical storage tank has a capacity of 200 tons. Currently, the tank contains 50 tons of a mixture that has 10% of a certain active chemical and 1.8% of other inert ingredients. The owners of the tank want to replenish the supply in the tank and will purchase some combination of two available mixes. Mix 1 contains 70% of the active chemical and 3% of the inert ingredients; its cost is $106 per ton. Mix 2 contains 30% of the active chemical and 1% of the inert ingredients; its cost is $42 per ton. The desired final mixture should have at least 40% of the active chemical and at most 2% of the inert ingredients. How many tons of each mix should be purchased to obtain the desired final mixture at minimum cost? Find the minimum cost. Note that at least 40% of the active chemical means; .

A) Minimum cost is $9,940 obtained by purchasing 70 tons of mix 1 and 60 tons of mix 2.
B) Minimum cost is $8,460 obtained by purchasing 60 tons of mix 1 and 50 tons of mix 2.
C) Minimum cost is $7,180 obtained by purchasing 40 tons of mix 1 and 70 tons of mix 2.
D) Minimum cost is $8,880 obtained by purchasing 60 tons of mix 1 and 60 tons of mix 2.
E) Minimum cost is $10,260 obtained by purchasing 50 tons of mix 1 and 60 tons of mix 2.

Question

A chemical storage tank has a capacity of 200 tons. Currently, the tank contains 50 tons of a mixture that has 10% of a certain active chemical and 1.8% of other inert ingredients. The owners of the tank want to replenish the supply in the tank and will purchase some combination of two available mixes. Mix 1 contains 70% of the active chemical and 3% of the inert ingredients; its cost is $106 per ton. Mix 2 contains 30% of the active chemical and 1% of the inert ingredients; its cost is $42 per ton. The desired final mixture should have at least 40% of the active chemical and at most 2% of the inert ingredients. How many tons of each mix should be purchased to obtain the desired final mixture at minimum cost? Find the minimum cost. Note that at least 40% of the active chemical means; ​  .
​
A) ​Minimum cost is $9,940 obtained by purchasing 70 tons of mix 1 and 60 tons of mix 2. 
B) Minimum cost is $8,460 obtained by purchasing 60 tons of mix 1 and 50 tons of mix 2. 
C) Minimum cost is $7,180 obtained by purchasing 40 tons of mix 1 and 70 tons of mix 2. 
D) Minimum cost is $8,880 obtained by purchasing 60 tons of mix 1 and 60 tons of mix 2. 
E) Minimum cost is $10,260 obtained by purchasing 50 tons of mix 1 and 60 tons of mix 2.

Quizplus · Accepted Answer

The Answer of A chemical storage tank has a capacity of 200 tons. Currently, the tank contains 50 tons of a mixture that has 10% of a certain active chemical and 1.8% of other inert ingredients. The owners of the tank want to replenish the supply in the tank and will purchase some combination of two available mixes. Mix 1 contains 70% of the active chemical and 3% of the inert ingredients; its cost is $106 per ton. Mix 2 contains 30% of the active chemical and 1% of the inert ingredients; its cost is $42 per ton. The desired final mixture should have at least 40% of the active chemical and at most 2% of the inert ingredients. How many tons of each mix should be purchased to obtain the desired final mixture at minimum cost? Find the minimum cost. Note that at least 40% of the active chemical means; ​  .
​
A) ​Minimum cost is $9,940 obtained by purchasing 70 tons of mix 1 and 60 tons of mix 2. 
B) Minimum cost is $8,460 obtained by purchasing 60 tons of mix 1 and 50 tons of mix 2. 
C) Minimum cost is $7,180 obtained by purchasing 40 tons of mix 1 and 70 tons of mix 2. 
D) Minimum cost is $8,880 obtained by purchasing 60 tons of mix 1 and 60 tons of mix 2. 
E) Minimum cost is $10,260 obtained by purchasing 50 tons of mix 1 and 60 tons of mix 2.

A Chemical Storage Tank Has a Capacity of 200 Tons