In a development plan of a city, a contractor has taken a contract to construct certain houses for which he needs building materials like stones, sand etc. There are three firms A, B, C that can supply him these materials. At one time these firms A, B, C supplied him 40, 35 and 25 truck loads of stones and 10, 5 and 8 truck load of sand respectively. If the cost of one truckload of stone and sand are Rs 1200 and 500 respectively, then find the total amount paid by the contractor to each of these firms A, B, C separately.

Answer

Rs 53000; Rs 44500; Rs 34000 , respectively

Explanation

The total load of stone and sand supplied by A can be
represented by rew matrix `X_(1)` and cost of one truck load of
stone and sand can be represented by column matrix `Y_(1)`
` therefore X_(1) = [(40,10)], Y_(1) = [[1200],[500]]`
Total amount paid by contractor to `A = X_(1) Y_(1)`
` = [(40,10)] [[1200],[500]]`
`[48000+5000]`
`=[53000]`
`therefore` Amount paid by contractor to A is Rs 53000
Similarly for `B, X_(2) = [(35,5)], Y_(2) = [[1200],[500]]`
Total amount paid by contractor to `B= X_(2) Y_(2)`
`= [(35,5)][[1200],[500]]= [42000+ 2500]`
`= [44500]`
`therefore ` Amount paid by contractor to B is Rs 44500
Similarly for C,
`X_(3) = [(25,8)],Y_(3)=[[1200],[500]]`
Total amount paid by contractor to `C = X_(3) Y_(3)`
`= [(25, 8)] [[1200],[500]]`
`= [30000+4000] =[34000]`
`therefore` Amount paid by contractor to C is Rs 34000