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As an enterprising member of a large company, you have developed the idea for a new venture for the company.
As an enterprising member of a large company, you have developed the idea for a new venture for the company. The venture consists of the production of three new products that can be produced on machines already owned and operated by the company. You have done your research and are confident that you can sell as many as 100 of each of the three products using existing marketing tools available to the company. However, discussions with the marketing department of the company has led to the further conclusion that additional investments in marketing specific to these products could raise sales. The initial analysis suggests that, for each $100 investment in marketing, the maximum sales limit could be increased by 10 units. However, the impact on sales will not be felt until the year after. Thus, if $100 is invested in marketing in year 1 for Product A then the maximum sales for Product A would jump to 110 for years 2 and 3. Also note that if $100 is invested additionally in marketing in year 2 for Product A then the maximum sales for Product A would jump to 120 for year 3.
Your CEO is interested but somewhat cautious. As a result, he agrees to give you an initial budget of $75,000. Due to the resource requirements of others branches of the business, he can only provide you with 750 hours on each on the machines in the first year but, by year 2, that number will jump to 1500 hours on each machine. The CEO will determine whether to continue with the venture based on the available funds at the end of year 3. The table below provides you with all the information you need.
Your task is to build a three year plan so as maximize available funds at the end of the 3rd year.
queation: Develop and solve a LP model to help determine a 3 year plan for the business venture. (Hint: each year you actually have 3 options - produce, invest in marketing or hold onto your cash till the next year - leading to a total of 18 decision variables with 9 relating to production, 6 related to marketing and 3 relating to holding onto your cash. Moreover, in your constraints, make sure you keep track of cash flow in each year so that you are not spending money you don't have!)
