p2 DS 52

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52. 4349-!-item-!-187;#058&003856
For Manufacturer M, the cost C of producing x units of its product per month is given by C = kx + t, where C is in dollars and k and t are constants. Last month, if Manufacturer M produced 1,000 units of its product and sold all the units for k + 60 dollars each, what was Manufacturer M's gross profit on the 1,000 units?

(1) Last month, Manufacturer M's revenue from the sale of the 1,000 units was $150,000.

(2) Manufacturer M's cost of producing 500 units in a month is $45,000 less than its cost of producing 1,000 units in a month.

ans:E

[Huang Hsin-Yi]

C=1000k+t
revenue=1000(K+60)=1000k+60000
profit=(1000k+60000)-(1000k+t)=60000-t=?

(1)10000k+60000=150000 可求K,但無法解60000-t
(2)500k+t=1000k+t-45000 可求K,但無法解60000-t

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thank Hsin-yi