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 $107 per ton. Mix 2 contains 30% of the active chemical and 1% of the inert ingredients; its cost is $46 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 $10,250 obtained by purchasing 70 tons of mix 1 and 60 tons of mix 2.
B)Minimum cost is $8,720 obtained by purchasing 60 tons of mix 1 and 50 tons of mix 2.
C)Minimum cost is $7,500 obtained by purchasing 40 tons of mix 1 and 70 tons of mix 2.
D)Minimum cost is $9,180 obtained by purchasing 60 tons of mix 1 and 60 tons of mix 2.
E)Minimum cost is $10,555 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 $107 per ton. Mix 2 contains 30% of the active chemical and 1% of the inert ingredients; its cost is $46 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 $10,250 obtained by purchasing 70 tons of mix 1 and 60 tons of mix 2. 
B)Minimum cost is $8,720 obtained by purchasing 60 tons of mix 1 and 50 tons of mix 2. 
C)Minimum cost is $7,500 obtained by purchasing 40 tons of mix 1 and 70 tons of mix 2. 
D)Minimum cost is $9,180 obtained by purchasing 60 tons of mix 1 and 60 tons of mix 2. 
E)Minimum cost is $10,555 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 $107 per ton. Mix 2 contains 30% of the active chemical and 1% of the inert ingredients; its cost is $46 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 $10,250 obtained by purchasing 70 tons of mix 1 and 60 tons of mix 2. 
B)Minimum cost is $8,720 obtained by purchasing 60 tons of mix 1 and 50 tons of mix 2. 
C)Minimum cost is $7,500 obtained by purchasing 40 tons of mix 1 and 70 tons of mix 2. 
D)Minimum cost is $9,180 obtained by purchasing 60 tons of mix 1 and 60 tons of mix 2. 
E)Minimum cost is $10,555 obtained by purchasing 50 tons of mix 1 and 60 tons of mix 2.

A Chemical Storage Tank Has a Capacity of 200 Tons