7) x 1 denotes the no. of apple pies. x 2 denotes the no. of cherry pies. Constr

Question

7) x1 denotes the no. of apple pies.
x2 denotes the no. of cherry pies.
Constraints are:

i) x1 >= 0 (integers)
ii) x2 >= 0 (integers)
iii) x1 <= 0.4*(x1 + x2)

The third constraint is the important constraint, as it denotes the production constraint specified above.

6) X and Y denote whether to build a company in Japan and China respectively. And X and Y are binary variables. And two countries cannot be selected at the same time.

Constraints:
i) 0 <= X <= 1 (and X is an integer)
ii) 0 <= Y <= 1 (and Y is an integer)
iii) If X > 0 ; Y= 0
iv) If Y > 0 ; X = 0

The above constraints satisfy the conditions mentioned above, as If X > 0, it will be only 1 and Y is equal to 0. So factory will not be built in China. And the same logic applies for Y > 0, where X will be 0 and factory will not be built in Japan.

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Satish

Explanation / Answer

6. (0.2 points) Let X and Y denote whether or not to build a factory in Japan and China, respectively. Suppose that X and Y are both binary variables. We want to ensure that the two countries cannot be selected at the same time. Write down the constraint formulation. 7. (0.2 points) Suppose that we use xi to denote the number of apple pies to bake and 22 to denote the number of cherry pies to bake. If we want to make sure that the number of apple pies cannot exceed 40% of our combined total production, write down the constraint.

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