per week:

demand, q = -50x +700-----if selling price is x per shirt.

Total Cost, C = 100 +6*q

C(x) = 100 +6[-50x +700]

C(x) = 100 -300x +4200

C(x) = -300x +4300 ----------------answer.

Revenue = x*q

R(x) = x[-50x +700] = -50x^2 +700x

Profit = Revenue minus Cost

P(x) = R(x) -C(x)

P(x) = [-50x^2 +700x] -[-300x +4300]

P(x) = -50x^2 +700x +300x -4300

P(x) = -50x^2 +1000x -4300 ---------------answer.

---------------

q = -50x +700

If no demand, q=0,

50x = 700

x = 14

That means x < 14, to have some demand.

Say x = 13

q = -50(13) +700 = 50 shirts

P(13) = -50(13^2) +1000(13) -4300

P(13) = 250

Say x = 2(6) = 12

q = -50(12) +700 = 100 shirts

P(12) = -50(12^2) +1000(12) -4300

P(12) = 500

Say x = 11

q = -50(11) +700 = 150 shirts

P(11) = -50(11^2) +1000(11) -4300

P(11) = 650

Say x = 10

q = -50(10) +700 = 200 shirts

P(10) = -50(10^2) +1000(10) -4300

P(10) = 700

Say x = 9

q = -50(9) +700 = 250 shirts

P(9) = -50(9^2) +1000(9) -4300

P(9) = 650

Going down. So max profit is when price is 10 per shirt.

This is not asked. I'm only playing.