Constraint Systems Worksheets Grade 9

1. A company produces two models of laptops: Model A and Model B. The production facility has these constraints: The total number of laptops produced daily cannot exceed 200. At least 40 Model A laptops must be made to fulfill contracts. Due to component supply, Model B production cannot exceed 150 units. The profit is $80 for each Model A and $120 for each Model B. How many Model B laptops should be produced daily to maximize profit while satisfying all constraints?
2. Lena is designing a rectangular garden with a perimeter of 40 meters. She wants the length to be at least 3 meters more than the width, and the area must be at least 60 square meters. Write a system of inequalities that represents the constraints on the garden's dimensions, using l for length and w for width.
3. Mason is helping his family plan a rectangular vegetable garden. The garden must have a perimeter of no more than 28 meters. To ensure enough sunlight, the length must be at least 2 meters greater than the width. Also, to fit the vegetables they want to plant, the area must be at least 15 square meters. Write a system of inequalities that represents these constraints, using L for length and W for width.

…and 3 more problems

1. Isabella is buying snacks for a party. She has $72 to spend. Chips cost $7 per bag and drinks cost $2 per bottle. She needs at least 12 items total and at least 3 bags of chips. Write the system of inequalities that represents these constraints, using x for bags of chips and y for bottles of drinks.
2. Aroha is planning a community garden with two types of vegetable beds. She can spend at most $150 on materials. Each large bed costs $12 and each small bed costs $9. She needs at least 10 beds total and wants at least 3 large beds. Write the system of inequalities that represents these constraints, where x is the number of large beds and y is the number of small beds.
3. A music festival is planning food truck placement. They have space for at most 15 food trucks total. They need at least 4 dessert trucks to satisfy demand, and the number of savory trucks must be at least double the number of dessert trucks. The festival organizers want to maximize revenue, and they estimate each dessert truck generates $800 per day while each savory truck generates $1200 per day. How many dessert trucks should they allow to maximize daily revenue while satisfying all constraints?

…and 4 more problems

1. Emma is organizing a school fundraiser by selling handmade bracelets and keychains. Each bracelet requires 3 hours of labor and $5 in materials, while each keychain requires 1 hour of labor and $3 in materials. Emma has at most 45 hours of labor available and a budget of at most $105 for materials. She wants to make at least 3 keychains for every bracelet to meet demand, and she must make at least 5 bracelets. Write a system of inequalities that represents all possible numbers of bracelets (b) and keychains (k) Emma can produce.
2. Emma is organizing a school event with a budget of $300. She needs to buy pizzas ($15 each) and drinks ($5 each). She needs at least 10 pizzas and at least 20 drinks. Write the system of inequalities that represents these constraints, where x is the number of pizzas and y is the number of drinks.
3. Aisha is designing a rectangular stage for a school play. The stage must have a perimeter of 50 meters. She needs the length to be at least 5 meters more than the width to accommodate the set design. Additionally, the area must be at least 126 square meters to fit all the performers. Write a system of inequalities that represents these constraints, using L for length and W for width.

…and 3 more problems