Question

2. An importer purchases two types of baseball helmet: standard helmets cost $80 each and deluxe helmets cost $120 each. The importer wants to spend a maximum of $4800, and because of government protection to local industry, can import no more than 50 helmets. Suppose the importer purchases x standard helmets and y deluxe helmets. List the constraints on the variables x and y.​

Answer 1

Answer: the three constraints on the variables x and y are:

80x + 120y ≤ 4800

x + y ≤ 50

x ≥ 0, y ≥ 0

Explanation:

Cost Constraint: The importer wants to spend a maximum of $4800, so the cost of the purchased helmets should not exceed $4800. The cost of x standard helmets and y deluxe helmets can be calculated as 80x + 120y, so the constraint can be written as:

80x + 120y ≤ 4800

Quantity Constraint: The importer cannot import more than 50 helmets in total. Therefore, the sum of standard and deluxe helmets purchased cannot exceed 50. The constraint can be written as:

x + y ≤ 50

Non-negativity Constraint: The importer cannot purchase negative helmets, so the variables x and y should be non-negative. The constraint can be written as:

x ≥ 0, y ≥ 0

Thus, the three constraints on the variables x and y are:

80x + 120y ≤ 4800

x + y ≤ 50

x ≥ 0, y ≥ 0