SOLUTION: The ABC Company is a well-known toy manufacturer. They have just started a new operation on programmable toy robots. Three different types are considered, Soldier, Tarzan, and Do

Question 1155860: The ABC Company is a well-known toy manufacturer. They have just started a
new operation on programmable toy robots. Three different types are considered,
Soldier, Tarzan, and Dog. The total cost of production must be minimized. A unit of
Soldier, Tarzan and Dog costs $50, $30 and $20 respectively. No more than 100
Dogs can be produced per week and the total production of Soldier plus Tarzan must
not be less than 400 units. A warehouse with a capacity of 600 units is used to store
the produced toys. The size of the 3 types is exactly the same and hence will occupy
the same space in the warehouse.
Answer by ikleyn(52879)   (Show Source): You can put this solution on YOUR website!
.

            It is very strange formulation. It differs very much from standard Linear Programming formulations.

            I will explain it in my solution below. I suspect that there is/(there are) error/(errors) in the formulation.

            But I will solve the problem "as is", exactly as it is given.

Let S = # of Soldiers; T = # of Tarzans, D = # of Dogs.

The objective function is the production cost  C(S,T,D) = 50*S + 30*T + 20*D dollars to minimize.

Since we want to minimize, the constraints "from the upper" do not play any role.

Concretely, the constraint on capacity does not play any role, as well as the constraint on the number of Dogs.


The only constraint which really matters is the constraint

    S + T >= 400.


But since we want to minimize the production cost, we take T = 400 (more cheaper than S) and S = 0.

We also put D = 0.


So, the solution to the given problem is  T = 400, S = 0, D = 0.


It satisfies all conditions (constraints) and provides the minimum cost  C(0,400,0) = 30*400 = 12000 dollars.    ANSWER

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