Question

a goldsmith take 2 hours to make a wedding ring and 3 hours to make a necklace, he can work for a maximum of 15 hours. in a day, he has. for at least 3 rings and 2 necklaces. On each wedding ring, he makes a profit of 3000.00 naira and on each wedding necklace, a profit of 5000.00 naira. Assuming he makes x rings and y necklace. Write all the inequalities connecting x and y.

Answer 1

The goldsmith's production constraints are expressed as a system of inequalities, with conditions based on time limits and minimum production requirements of rings and necklaces, as well as the non-negativity of items produced.

Step-by-step explanation:

The goldsmith's time and profit constraints can be translated into several inequalities involving the number of rings (x) and necklaces (y) he can make. First, the time constraint for a maximum of 15 hours of work per day:

2x + 3y ≤ 15 (1)

He must make at least 3 rings and at least 2 necklaces:

x ≥ 3 (2)

y ≥ 2 (3)

Since he cannot make a negative number of rings or necklaces, we also have the non-negativity constraints:

x ≥ 0 (4)

y ≥ 0 (5)

To summarize, assuming the goldsmith makes x wedding rings and y necklaces, the following inequalities must hold:

• 2x + 3y ≤ 15
• x ≥ 3
• y ≥ 2
• x ≥ 0
• y ≥ 0