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QUESTIONJUL 29, 2018A company produces 4 types of central heating radiator, known as types A, B, C and D. A builder buys radiators for all the houses on a new estate.

A company produces 4 types of central heating radiator, known as types A, B, C and D.A builder buys radiators for all the houses on a new estate. There are 20 small houses, 30medium-sized houses and 15 large houses.(a) Represent the number of small, medium-sized and large houses using a 1 × 3 matrix.(b) A small house needs 3 radiators of type A, 2 of type B and 2 of type C. A medium-sizedhouse needs 2 radiators of type A, 3 of type C and 3 of type D. A large house needs 1radiator of type A, 6 of type C and 3 of type D. Use a 3 × 4 matrix to represent thenumber of radiators of type A, B, C and D needed for each type of house.(c) The cost of each type of radiator is $30 for type A, $40 for type B, $50 for type C and $80for type D. Represent the cost of each type of radiator using a 4 × 1 matrix.(d) Using matrix multiplication twice, find the total cost to the builder of all the radiators forthe estate.