a landscape contractor is hired to cultivate ornamental plants in three new residential developments. the contractor charges the developer for each tree cultivated,an hourly rate to cultivate the ornamental plants, and a fixed delivery charge. in one development it took 211 labour hours to cultivate 244 ornamental plants for a cost of $9394. in a second development it took 128 labour hours to cultiv ate 283 ornamental plants for a cost of $8270. in the final development it took 165 labour hours to cultivate 386 ornamental plants for a cost of $10938. in total 504 labour hours were taken and 913 ornamental plants were cultivated. using cramer's rule of the inverse method, determine the cost for each tree, the hourly labour charge and the delivery charge.
a landscape contractor is hired to cultivate ornamental plants in three new residential developments. the contractor charges the developer for each tree cultivated,an hourly rate to cultivate the ornamental plants, and a fixed delivery charge. in one development it took 211 labour hours to cultivate 244 ornamental plants for a cost of $9394. in a second development it took 128 labour hours to cultiv ate 283 ornamental plants for a cost of $8270. in the final development it took 165 labour hours to cultivate 386 ornamental plants for a cost of $10938. in total 504 labour hours were taken and 913 ornamental plants were cultivated. using cramer's rule of the inverse method, determine the cost for each tree, the hourly labour charge and the delivery charge.
Let rate per rose = $x1
Let rate per hour = $x2
let fixed rate = $x3
So according to question we have
244x1 + 211x2 +x3 = 9394
283x1 + 12x2 + x3 = 8270
386x1 + 165x2 + x3 = 10938
Let us use cramers rule her
The determinant of the above matrix = 9992
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