# Science:Math Exam Resources/Courses/MATH105/April 2011/Question 06

MATH105 April 2011
Other MATH105 Exams

### Question 06

A certain T-shirt company makes two types of shirts. Type A says "Much Music rocks" while Type B says "Business Calculus rocks". The company produces 1000 T-shirts in total every year. It sells each Type A shirt at $15 and each Type B shirt at$10. If the cost of producing ${\displaystyle x}$ shirts of Type A and ${\displaystyle y}$ shirts of Type B is

${\displaystyle C={\frac {1}{200}}x^{2}+6x+4y+4000,}$

determine how many shirts of each kind the company should produce to maximize its profit every year. Give a simple justification why the answer you obtained gives the maximum and not the minimum.

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