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Hey guys, Im not sure if this is really a business math question so sorry if it’s in the wrong thread, but I really need some help with this question;
A chocolate manufacturer produces two types of of chocolate bar, NomNoms and Tasty Bars. The manufacturer uses two factories, and both factories can produce both chocolate bars.
The maximum daily output at factory 1 is 5000 chocolate bars, and due to the factorys' production costs, the profit for NomNom bars is 5p per bar and for TastyBars is 6p per bar. At factory 2, the maximum daily output is 8000 chocolate bars, and the profits are 4p per NomNom and 8p per TastyBar. In addition, restrictions at factory 1 mean that the number of NomNoms produced cannot fall below 1500 bars less than the number of tasty bars produced.
An order is recieved for 5000 NomNoms and 6000 Tasty Bars.
Let x denote the number of NomNoms and y denote the number of TastyBars manufactured at factory 1.
(a) Explain why the number of chocolate bars ti be produced at factory 2 is (5000-x) NomNoms and (6000-y) TastyBars
(b) Show that an expression for the profit on the order, in pence, is given by P=x-2y+68000
(c) Write down all of the constraints for the problem
(d) Solve the linear programming problem graphically to find the number of each type of chocolate bar to produce at factory 1 in order to maximise the profit. On your graph indicate clearly the feasible region, the optimal point, an arbitrary isoprofit line, and the isoprofit line corresponding to the optimal point.
(e) Hence state the optimum number of each type of chocolate bar to produce at each factory, and the maximum profit that can be made.
Any help would be much appreciated and sorry for the length of the question!
Thanks in advance!