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Question
A company wants to know when the sale of their product reaches a profit level of Rs. 1000. The revenue equation is R = 200x−0.5x2, and the cost to produce x product is determined with C=−6000−40x. How many products have to be produced and sold to net a profit of Rs. 1000?
A company wants to know when the sale of their product reaches a profit level of Rs. 1000. The revenue equation is R = 200x−0.5x2, and the cost to produce x product is determined with C=−6000−40x. How many products have to be produced and sold to net a profit of Rs. 1000?
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Solution
The correct option is D 500
The amount of the profit is determined by subtracting the cost from the revenue, P=R−C.
1000= 200x−0.5x2−(−6000−40x)
1000= 200x−0.5x2+6000+40x)
0.5x2−240x−5000
On factoring, we get
(x−500)(x+20)=0
x=500 or −20
When x=500, the profit is 1000.
The amount of the profit is determined by subtracting the cost from the revenue, P=R−C.
1000= 200x−0.5x2−(−6000−40x)
1000= 200x−0.5x2+6000+40x)
0.5x2−240x−5000
On factoring, we get
(x−500)(x+20)=0
x=500 or −20
When x=500, the profit is 1000.
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