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Linear Programming.

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Introduction

Linear Programming Our school is planning to introduce house t-shirts for each of the four houses, however, they have set the task of obtaining the t-shirts to each individual house. Our house, Garrett Anderson, has 85 people, and we thought that it would be cheaper to share the price of the t-shirts with another house, Fry. Garrett Anderson t-shirts would be white, the house colour, with the house logo on it, and Fry would be purple, with their house logo on it. Fry need 70 t-shirts. It costs �5 to buy each white t-shirt and an extra �0.75 each t-shirt to be dyed the purple colour. It costs an extra �1.00 to buy a large sized t-shirt, regardless of colour. It is optional for years 11-13 to buy a t-shirt, but if we buy 100+ t-shirts, we receive a 10% discount, but if we buy 150+ t-shirts, we receive a 15% discount. The overall cost would be shared between the two houses. However, I complied a new question, as this did not complete the criteria of the coursework having a profit function and it became quite complicated as Problem Two My house Garrett Anderson needs house t-shirts with the house logo printed on it. Our school has given us �800 to buy them. ...read more.

Middle

Therefore the x co-ordinate is 50. Substituting 50 into the equation to find the y co-ordinate: 50 = 3y y = 16 2/3 Therefore the point is (50, 16 2/3). Vertice 3: This is where the lines x > 3y and 4x + 5y < 800 cross. To find the y co-ordinate: x = 3y 4x = -5y + 800 Multiply the first equation by 4 4x = 12y 4x = -5y + 800 = -17y +800 y = 800 17 y = 47.06 (to 2 d.p.) Substituting the y co-ordinate into the first equation: x = 3 (47.06) x = 141.18 Therefore the point is (141.18, 47.06). Vertice 4 This is the point where the equation 4x + 5y < 800 meets the x axis. Therefore y is 0 so to find the y co-ordinate: 4x = 800 x = 800 4 x = 200 Therefore the point is (200, 0). In order to calculate profit, the equation: 6x + 8y+ = m where m equals the amount of money we would make from selling the t shirts. We must calculate first how much the t-shirts cost to make, and subtract this from how much money we would make by selling the t-shirts. (6x + 8y) - (4x + 5 y) ...read more.

Conclusion

- (4.50x + 5.50y) Simplified: p = 2x +3y This is the same as the original as we have -------------------------------------------------------------------------------- Education E Mail This message is for the named person's use only. It may contain confidential, proprietary or legally privileged information. No confidentiality or privilege is waived or lost by any mistransmission. If you receive this message in error, please immediately delete it and all copies of it from your system, destroy any hard copies of it and notify the sender. You must not, directly or indirectly, use, disclose, distribute, print, or copy any part of this message if you are not the intended recipient. The States of Jersey Education Committee and any of its establishments each reserve the right to monitor all e-mail communications through its networks. Any views expressed in this message are those of the individual sender, except where the message states otherwise and the sender is authorised to state them to be the views of any such entity. The States of Jersey Education Committee shall not be liable to the recipient or any third party for any loss or damage, however it appears, from this e-mail or its content. This includes loss or damage caused by viruses. It is the responsibility of the recipient to ensure that the opening of this message and its attachments shall not adversely affect systems or data. ...read more.

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