Q A screen printer produces custom silkscreen apparel The pr

Q:

A screen printer produces custom silk-screen apparel. The profit P(x) from the sale of x T-shirts in dollars is given by P(x) = -0.05x² + 7.75x - 200

Determine the number of T-shirts that should be produced to result in the maximum profit and find the maximum profit. (Note: Only whole T-shirts are produced.)

Solution

profit P(x) from the sale of x T-shirts in dollars is given by P(x) = -0.05x2 + 7.75x - 200

P(x) is a quadratice function

Maximum point lies at vertex given by x = -b/2a = -( 7.75)/2( -0.05) = 77.5 = 77 t shirts

Maximum Profit is found by plugging x= 77 in P(x) = -0.05(77)^2 +7.75(77) -200

= $100.3

=