Problema Solution
the cost C of manufacturing n calculators per day at a certain plant is given by C=n(20-0.01n)+100. The size of the plant limits the maximum output to 500 calculators per day. If the company plans to invest 5200 dollars per day in manufacturing costs, how many calculators per day can it manufacture?
Answer provided by our tutors
n = the number of calculators per day
C=n(20-0.01n)+100 the cost for making n calculators per day
the size of the plant limits the maximum output to 500 calculators per day
n <=500
the company plans to invest 5200 dollars per day in manufacturing costs and the cost is calculated by C=n(20-0.01n)+100 thus
n(20-0.01n)+100 = 5200
20n - 0.01n^2 + 100 - 5200 = 0
- 0.01n^2 + 20n - 5100 = 0 multiply both sides by -1/0.01
n^2 - 2000n + 510000 = 0
by solving the quadratic equation we find 2 roots
n1 = 300
n2 = 1700
since n<=500 the solution is n = 300 calculators per day.
click here to see the step by step solution of the quadratic equation