Math Problem Statement
Solution
The problem you shared is an optimization problem related to maximizing profits in production, based on resource constraints. Here's a breakdown of the problem:
Variables:
- Let represent the number of sweet bread ("roti manis") produced.
- Let represent the number of plain bread ("roti tawar") produced.
Resource Constraints:
-
Flour (terigu):
- Sweet bread uses 20g per unit.
- Plain bread uses 40g per unit.
- The maximum available flour is 8000g (8 kg).
- Constraint:
-
Margarine:
- Sweet bread uses 20g per unit.
- Plain bread uses 20g per unit.
- The maximum available margarine is 6000g (6 kg).
- Constraint:
-
Sugar (gula):
- Sweet bread uses 20g per unit.
- Plain bread uses no sugar.
- The maximum available sugar is 5000g (5 kg).
- Constraint:
Objective Function (Profit):
- Sweet bread gives a profit of Rp 1,100 per unit.
- Plain bread gives a profit of Rp 900 per unit.
- The objective is to maximize total profit:
Constraints Summary:
- (Flour constraint)
- (Margarine constraint)
- (Sugar constraint)
Additionally, and .
Would you like me to proceed with solving this optimization problem to find the values of and for the maximum profit?
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Formulas
Maximize Z = 1100x + 900y
20x + 40y ≤ 8000 (Flour constraint)
20x + 20y ≤ 6000 (Margarine constraint)
20x ≤ 5000 (Sugar constraint)
Theorems
Linear Programming Optimization
Suitable Grade Level
High School (Grades 10-12)
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