Grade 12 Math: Resource Allocation
A Grade 12 math worksheet focusing on resource allocation, including linear programming, budget constraints, and optimization problems.
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Resource Allocation Worksheet
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Read each question carefully and provide detailed answers. Show all your work for calculations.
1. Which of the following best describes the primary goal of resource allocation?
Maximizing production regardless of cost.
Distributing resources to achieve optimal outcomes.
Minimizing resource consumption at all times.
Ensuring equal distribution among all parties.
2. In linear programming, what does the 'objective function' represent?
The limitations on available resources.
The quantity to be maximized or minimized.
The feasible region of solutions.
The non-negativity constraints.
1. The process of making decisions on how to best use available resources to achieve specific goals is known as .
2. A common method for solving optimization problems with linear constraints is called .
3. In a budget, are costs that remain constant regardless of the level of activity.
1. A company produces two types of widgets, A and B. Widget A requires 2 hours of labor and 1 kg of raw material. Widget B requires 3 hours of labor and 0.5 kg of raw material. The company has 120 hours of labor and 40 kg of raw material available. If the profit for Widget A is $15 and for Widget B is $20, formulate the objective function and constraints to maximize profit.
2. Explain the concept of a 'feasible region' in the context of linear programming and its importance in resource allocation.
1. Scarcity of resources is a fundamental concept in resource allocation.
True
False
2. Opportunity cost refers to the direct financial cost of a decision.
True
False
1. A small business makes two types of handcrafted jewelry: necklaces and bracelets. Each necklace requires 20 minutes to make and $5 in materials. Each bracelet requires 10 minutes to make and $3 in materials. The business has a total of 10 hours of labor available per week and a material budget of $200 per week. If the profit from each necklace is $12 and from each bracelet is $7, determine the number of necklaces and bracelets the business should make to maximize its profit. Graph the feasible region and identify the optimal solution.