The Intellectual Company produces a chemical solution used for cleaning carpets. This chemical is made from a mixture of two other chemicals which contain cleaning agent X and cleaning agent Y. Their product must contain 175 units of agent X and 150 units of agent Y and weigh at least 100 pounds. Chemical A costs ₱ 8 per pound, while chemical B costs ₱ 6 per pound. Chemical A contains one unit of agent X and three units of agent Y. Chemical B contains seven units of agent X and one unit of agent Y. a. Set up the following: i. Variables ii. Constraints iii. Objective Function b. Find the minimum cost c. Determine the best combination of the ingredients to minimize the cost.
The Intellectual Company produces a chemical solution used for cleaning carpets. This chemical is made from a
mixture of two other chemicals which contain cleaning agent X and cleaning agent Y. Their product must contain
175 units of agent X and 150 units of agent Y and weigh at least 100 pounds. Chemical A costs ₱ 8 per pound,
while chemical B costs ₱ 6 per pound. Chemical A contains one unit of agent X and three units of agent Y.
Chemical B contains seven units of agent X and one unit of agent Y.
a. Set up the following:
i. Variables
ii. Constraints
iii. Objective Function
b. Find the minimum cost
c. Determine the best combination of the ingredients to minimize the cost.
2. The Guinevere Corporation is trying to establish a transportation system of small and large vans. It can spend no
more than ₱ 100,000 for both sizes of vehicles and no more than ₱ 500 per month for maintenance. The Corporation can
purchase a small van, which carries up to 7 passengers, for ₱ 10,000 and maintain it for ₱ 100 per month. The large vans,
which carry up to 15 passengers, cost ₱ 20,000 each and can be maintained for ₱ 75 per month.
a. Set up the following:
i. Variables
ii. Constraints
iii. Objective Function
b. How many of each type of van should they purchase if they want to maximize the number of passengers
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