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A real estate developer is planning to build an office complex. Currently, there are three office sizes under consideration: small, medium, and large. Small offices can be rented for $600 $ per month
medium offices can be rented for $750 $ per month, and large offices can be rented for $1000 $ per month. Each small office requires 600 square feet, each medium office requires 800 square feet, and each large office requires 1000 square feet. The current plot of land available to the developer is 100,000 square feet. The developer wants to ensure that the office complex has at least 3 units of each office size. Moreover, zoning restrictions limit the total number of offices to 50.

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$ I\ think\ the \ formulation \ of \ the \ problem \ is \\ Max \ Z=660 x_{1}+750 x_{2}+1000x_{3}. \\ Subject \ to \ the \ conditions, \\ x_{1}\geq 3, \\ x_{2}\geq 3, \\ x_{3} \geq 3, \\ x_{1}+x_{2}+x_{3}\leq 50 \ and \\ 600 x_{1}+800 x_{2} +1000x_{3} \leq 100000, \\ x_{i}\geq 0, i=1,2,3. \\ $ $$ $$ Some one please help me is the above formulation is right , because i am having problem to solve this.

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    This is not a forum. Here, answers are real answers. You can answer yourself, but this is not an answer. Please edit this answer, copy it and paste it into your question. (Yes, you can edit your question). Then, delete this answer. – 2017-02-06
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    You should edit this into the question to show the work you have done. They look like the correct equations to me. Where are you having trouble solving them? Certainly $x_1=x_2=x_3=3$ is a feasible solution. – 2017-02-06