Question

Your company purchases two cleaning products, A and B. Your cost to buy Product A is $3 per ounce, and your cost to buy Product B is $2 per ounce. Product A contains 1 unit of ammonia per ounce and 2 units of alcohol per ounce. Product B contains 3 units of ammonia per ounce and 1 unit of alcohol per ounce. You mix some of Product A and Product B to make a cleaning product which meets your company’s needs. You need your special mix to contain at least 6 units of ammonia and 3 units of alcohol. How much should you order of each product to minimize your cost? Problem 8. What is the objective function for this problem? Select the best answer, and fill in the appropriate bubble on the provided bubble shee

Answer 1

The objective function is
`\( C(x, y) = 3x + 2y \)` representing the cost of mixing cleaning products A and B
`(cost $3/oz and $2/oz, respectively)`to meet ammonia and alcohol requirements.

To formulate the objective function for this problem, let \( x \) represent the number of ounces of Product A and \( y \) represent the number of ounces of Product B.

The cost of Product A is $3 per ounce, and the cost of Product B is $2 per ounce. Therefore, the cost function can be expressed as:

`\[ C(x, y) = 3x + 2y \]`

The objective is to minimize the cost while meeting the requirements for ammonia and alcohol. The problem states that the mix should contain at least 6 units of ammonia and 3 units of alcohol.

The units of ammonia in the mix are
`\( x + 3y \)` (1 unit per ounce for Product A and 3 units per ounce for Product B).

The units of alcohol in the mix are
`\( 2x + y \)`(2 units per ounce for Product A and 1 unit per ounce for Product B).

The constraints for the problem are:

`\[ x + 3y \geq 6 \]`(at least 6 units of ammonia)

`\[ 2x + y \geq 3 \]`(at least 3 units of alcohol)

These constraints are inequalities because the mix should contain "at least" the specified amounts.

In summary, the objective function for this problem is the cost function:

`\[ C(x, y) = 3x + 2y \]`