SOLUTION: In producing a new product a manufacturer predicts that the number of items produced x and the cost in dollars C of producing those items will be related by a linear model. The cos

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Question 437332: In producing a new product a manufacturer predicts that the number of items produced x and the cost in dollars C of producing those items will be related by a linear model. The cost of producing 100 items will be related $5000 and the cost of producing 500 items is $15000. Find the linear model relating z and C. Use the model to predict the cost for producing 400 items.
Use the model to predict the number of items that can be produced with $18000.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi 

(500,15000)    |Using the point-slope formula, m+=%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

(100,5000)  m = 10,000/400 = 25



Using the standard slope-intercept form for an equation of a line y = mx + b

  where 25 is the slope and b the y-intercept.  

 C(x) = 25x + b

 5000 = 25*100 + b   |Using ordered pair (100,5000) to solve for b

 2500 = b

 C(x) = 25*x + $2500    

 C(400) = 25*400 + $2500 = $12,500



$18,000 = 25x + $2500

 15500/25 = x = 620 items would be predicted to be produced with $18,000