please solve with the given information

2. Fish In Tanks (FIT) are a company that manufactures ready made and populated fish tanks. FIT can sell all the tanks that they make. FIT makes three different kinds of tank, these are Salt Water, Fresh Water, and Turtle. The profit contributions (after all raw material and labour costs have been deducted) of these tanks are $200, $140, and $300 (each) FIT wants to schedule the production of these tanks to maximise their profit on a daily basis. Each type of tank requires Glass and Filters, costs a certain amount for Raw Materials, and uses a certain amount of Labour. These are given by the following table. Glass (kg/item) Filters (/item) Raw Materials ($/item) Labour (h/item) Salt Water Fresh Water Turtle 4 3 2 1 2 0 20 30 50 2 1 2 As a preliminary exercise you have been asked to prepare a schedule for tomorrow's production. For this, FIT have ordered 30 kg of Glass, 12 Filters, and can spend $250 in Raw Materials. They employ 2 people who each work an 8 hour shift. (a) Formulate the problem of planning tomorrow's production to maximize profit as a linear programming problem. (b) The production planning problem was input to EXCEL and the output is shown below (last pages of this document). As the Operations Research consultant employed by FIT you have been asked to give a presentation on the model. Answer the following questions, making explicit reference to the EXCEL out- put where necessary (you may assume that fractional numbers of tanks can be produced). i. What profit can FIT expect to make tomorrow from the optimal production plan? ii. How many of each type of tank should they make? iii. Should the company spend more money on Raw Materials? If so how much more profit will FIT make for each additional dollar spent? iii. Should the company spend more money on Raw Materials? If so how much more profit will FIT make for each additional dollar spent? iv. FIT finds that they can buy more Filters for tomorrow. What is the maxi- mum price they should pay for these Filters? v. How much profit do we need to make on each Fresh Water tank before it becomes optimal to make Fresh Water tanks. vi. FIT wishes to hire another worker, for an 8 hour shift, and pay them $150 a day more than the other two workers. If everything else is kept the same can you recommend this? vii. If the profit from Salt Water tanks rose to $250 dollars what would be the new optimal production plan and daily profit? viii. If the profit on Turtle tanks fell to $200 dollars what would be the new optimal production plan and profit? Target Cell (Max) Cell Name $A$5 Obj Original Value 0 Final Value 1900 Adjustable Cells Cell Name $B$2 Salt Water $C$2 Fresh Water $D$2 Turtle Original Value 0 0 0 Final Value 5 0 3 Slack Constraints Cell Name $F$7 Glass 4 Cell Value Formula Status Not 26 $F$7