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(a)A company uses resources A and B to manufacture three components,ampli-

By December 6, 2021No Comments

(a)A company uses resources A and B to manufacture three components,ampli-fiers,modulators and oscillators.These components are then combined intoproducts a and B.There are 600 units of resource A and 500 units of resource B available eachday.One amplifier requires 3 units of resource A and 3 units of resource B.One modulator requires 4 units of resource A and 5 units of resource B.Oneoscillator requires 4 units of resource A and 2 units of resource B.One unit of product a requires one amplifier,two modulators and three oscillators,One unit of product B requires three amplifiers,two modulators andfive oscillators.One unit of product a sells for a profit of f10 and one unit of product B sellsfor a profit of£l3.Write a linear programming problem to decide how many of each componentand each product to make each day.You must explain any notation youintroduce,and explain your constraints and objective function.(Do not attempt to solve the linear programming problem.You mayignore any need to produce whole numbers of items.)10 marks](b)The situation is actually a bit more complicated.The components are createdat a component manufacture site,and the products are created at separateproduct manufacture (PM)sites.Product a is made at PM site a and productB is made at PM site B.The components must be sent to the product manufacture sites,and this incursa transportation cost.Each amplifier costs£I to send to PM site a.and£lto send to PM site B.Each modulator costs f4 to send to PM site a and f2to send to PM site B.Each oscillator costs f2 to send to PM site a and flto send to PM site B.Write a linear programming problem to address this new problem.You may as-sume that sending components to sites is instantaneous.You must explain anynotation you introduce,and explain your constraints and objective function.(Do not attempt to solve the linear programming problem.You mayignore any need to produce whole numbers of items.)(5 marks(c)Suppose for this part that all transportation costs are zero.(i)Without solving the LPPs.answer the following question.Is the optimalvalue of your LPP in (a)less than,greater than,or equal to the optimalvalue of your LPP in (b)?Justify your answer mathematically.2 marks(ii)How does your answer to (i)change if we require that whole numbers ofcomponents and products are produced?Justify your answer mathemati-cally.(3 marks

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