A manufacturer sells three types of containers, ranging from 18 to 30 cubic feet in volume....

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A manufacturer sells three types of containers, ranging from 18 to 30 cubic feet in volume. The size and demand of each type of containers are as follows: 12 3 26 30 type Size Demand 400 500 400 18 That is, there is a demand of 400 containers of type 1, 500 containers of type 2, etc. The unit cost of producing each container is equal to ten times the volume of the container. (For example, to produce one container of type 1, the cost is $10x30 = $300.) A fixed setup cost of S10,000 is required to produce a type of container. Also, demand for a container can be satisfied by a container of larger size. (For example, the manufacturer could decide to make 900 containers of type 1 and 400 containers of type 3. [Note that among the 900 containers of type 1, 500 of them could be used to satisfy the demand of containers of type 2.] The total cost in the case would be: (1x$10,000 + $900×30) + (0x$10,000 + S0x26) + (1×$10,000 + $400x18).) The manufacturer wants to minimize the total cost. Formulate a corresponding integer program. Your integer program should contain no more than six constraints. Write down the meaning of each variable. A manufacturer sells three types of containers, ranging from 18 to 30 cubic feet in volume. The size and demand of each type of containers are as follows: 12 3 26 30 type Size Demand 400 500 400 18 That is, there is a demand of 400 containers of type 1, 500 containers of type 2, etc. The unit cost of producing each container is equal to ten times the volume of the container. (For example, to produce one container of type 1, the cost is $10x30 = $300.) A fixed setup cost of S10,000 is required to produce a type of container. Also, demand for a container can be satisfied by a container of larger size. (For example, the manufacturer could decide to make 900 containers of type 1 and 400 containers of type 3. [Note that among the 900 containers of type 1, 500 of them could be used to satisfy the demand of containers of type 2.] The total cost in the case would be: (1x$10,000 + $900×30) + (0x$10,000 + S0x26) + (1×$10,000 + $400x18).) The manufacturer wants to minimize the total cost. Formulate a corresponding integer program. Your integer program should contain no more than six constraints. Write down the meaning of each variable.