Question

What are the resource inequalities for the following situation? Producing a bookshelf requires 6 boards and 14 screws. Producing a TV stand requires 10 boards and 16 screws. Each bookshelf yields $27 profit, and each TV stand yields $24 profit. There are 65 boards and 120 screws available. 6x+14y≤65,10x+16y≤120,x≥0,y≥06x+10y≤65,14x+16y≤120,x≥0,y≥06x+10y≤27,14x+16y≤24,x≥0,y≥06x+14y≤27,10x+16y≤24,x≥0,y≥0​

Answer 1

The resource inequalities for producing bookshelves and TV stands can be represented by the equations 6x + 14y ≤ 65 and 10x + 16y ≤ 120, where x represents the number of boards and y represents the number of screws.

Step-by-step explanation:

The resource inequalities for this situation can be represented by the following equations:

• 6x + 14y ≤ 65
• 10x + 16y ≤ 120
• x ≥ 0
• y ≥ 0

These equations represent the constraints on the number of boards (x) and screws (y) available to produce bookshelves and TV stands. The first equation ensures that the total number of boards and screws used for producing bookshelves does not exceed the available quantity, while the second equation ensures the same for TV stands. The last two inequalities specify that the quantities of boards and screws used cannot be negative.