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Question 152913This question is from textbook introductory mathematical analysis , for business ,economics and the life and social science
: Hi iam having some problems with this question, i would appreciate it very much if you could solve it for me, thank you.
Equalizing cost.
United products co. manufactures calculators and has plants in the cities of Exton AND WHYTON .At the Exton plant, fixed cost are $7000 per month , and cost of producing each calculator is $7.50.At the Whyton plant ,fixed cost are $8800 per month ,and each calculator costs $6.00 to produce .Next month ,United products must produce 1500 calculators.How many must be made at each plant if the total cost at each plant is be the same
This question is from textbook introductory mathematical analysis , for business ,economics and the life and social science
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let E = the monthly cost at the Exton plant to produce x calculators.
Let W = the monthly cost at the Whyton plant to produce (1500-x) calculators.
As you can see, the number of calculators produced by the two plants together is (x+ (1500-x) = 1500).
Let's write the equations for the monthly cost at each plant:
E = $7000+($7.50)(x) This is the cost at the Exton plant.
W = $8800+($6.00)(x) This is the cost at the Whyton plant.
The problem asks "how many calculators should be produced at each plant if the total cost is to be the same at each plant.
So we set E = W and solve for x and then 1500-x.
$7000+$7.50(x) = $8800+$6.00(1500-x) Simplify and solve for x.
7000+7.5x = 8800+9000-6x
7000+7.5x = 17800-6x Subtract 7000 from both sides.
7.5x = 10800-6x Add 6x to both sides.
13.5x = 10800 Finally, divide both sides by 13.5
x = 800 and (1500-x) = (1500-800) = 700
So the Exton plant must produce  calculators and the Whyton plant must produce  calculators for a total of 1500 calculators for the total cost at each plant to be the same.
Check:
E = $7000+$7.50(800) = $7000+$6000 = $1300
W = $8800 +$6.00(700) = $8800+$4200 = $1300
The cost is the same at each plant!
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