Set up the objective function and the constraints, but do not solve. Chemical Products makes two insect repellents, Regular and Super. The chemical used for Regular is 15% DEET, and the chemical used for Super is 25% DEET. Each carton of repellent contains 24 ounces of the chemical. In order to justify starting production, the company must produce at least 14,000 cartons of insect repellent, and it must produce at least twice as many cartons of Regular as of Super. Labor costs are $9 per carton for Regular and $4 per carton for Super. How many cartons of each repellent should be produced to minimize labor costs if 70,680 ounces of DEET are available? (Let x represent the number of cartons of Regular, y the number of cartons of Super, and z the labor costs in dollars.) z = , subject to total production ratio of carton type amount of DEET x ≥ 0, y ≥ 0
Set up the objective function and the constraints, but do not solve.
Chemical Products makes two insect repellents, Regular and Super. The chemical used for Regular is 15% DEET, and the chemical used for Super is 25% DEET. Each carton of repellent contains 24 ounces of the chemical. In order to justify starting production, the company must produce at least 14,000 cartons of insect repellent, and it must produce at least twice as many cartons of Regular as of Super. Labor costs are $9 per carton for Regular and $4 per carton for Super. How many cartons of each repellent should be produced to minimize labor costs if 70,680 ounces of DEET are available? (Let x represent the number of cartons of Regular, y the number of cartons of Super, and z the labor costs in dollars.)
| z = |
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, subject to |
| total production |
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|
| ratio of carton type |
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| amount of DEET |
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| x ≥ 0, y ≥ 0 |
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