4. (a) An engineer is in the process of constructing two straight roads, RI and R, which will meet at the right angles. If RI will be represented by the equation 2x—3y—4=0 and R, will pass through the point , find the equation representing R2 in the form ax+by+c=0
(b) A boat crosses a river at a velocity of 30 km/h southwards. Water in the river flows at 5 km/h due East. By using the knowledge of vectors, calculate the resultant velocity of the boat. Give the answer correct to 2 decimal places.
(b) The mass (M) which can be supported by a beam varies directly with the breadth (b) and inversely with the length (l). If a beam of breadth 2 m and length 15 m can support a mass of 200 kg, what mass can be supported by a beam which is 3 m broad and 20 m long?
14. (a) Jennifer makes two types of garments, Batiki and Kitenge. Batiki requires 2.5 metres of material while Kitenge requires 2 metres of material. The business uses up to 400 metres of materials daily for the production of both types of garments but produces at most 80 metres of Batiki and at least 60 metres of Kitenge daily. Taking x to represent the number of Batiki and y the number of Kitenge produced daily;
(i) write down the inequalities satisfying the given information.
(ii) find the number of each type of garments the business can produce in order to get the maximum income if the income is given by f (x, y) = 300x+ 200y .
(b) What is the importance of studying linear programming? Give 2 points.