$7.$ A refinery's catalytic cracker processes $200,000$ barrels of feedstock per month, producing $35\%$ gasoline, $25\%$ diesel, and $40\%$ other products. Calculate the monthly production of diesel in barrels.

a$)50,000$ barrels

b$)55,000$ barrels

c$)60,000$ barrels

d$)65,000$ barrels