Constraints Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardA farmer plants corn (\200/acre profit) and soybeans (\150/acre profit) on at most 100 acres, with at least 20 acres of corn. Write the constraints and find the profit-maximizing allocation.
Solution
- 1 Let \(c\) = corn acres, \(s\) = soybean acres.
- 2 Constraints: \(c + s \leq 100\), \(c \geq 20\), \(s \geq 0\).
- 3 Profit: \(P = 200c + 150s\).
- 4 Since \200 > \150, maximize corn. Set \(c = 100, s = 0\) (if \(c \geq 20\) met): \(P = 200(100) = \$20{,}000\).
- 5 Optimal: 100 acres of corn, 0 soybeans.
Answer
100 acres corn, 0 soybeans; profit = \$20,000
Maximize by allocating all land to the higher-profit crop (corn, \$200/acre) while satisfying all constraints.
About Constraints
Conditions or restrictions that limit which values are allowed in a problem. Constraints narrow the set of possible solutions, such as 'x must be positive' or 'the total cannot exceed 100.'
Learn more about Constraints โMore Constraints Examples
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You have [formula]3 each) and pens ($2 each). Write the constraint inequality and find a valid combi
Example 3 mediumA box must hold at least 10 items but no more than 25 items. Write this as a compound inequality and
Example 4 hardA recipe needs at least 2 cups of flour and no more than 5 cups total of flour and sugar combined. I