Given the cost function in dollars Cx y 300 2x 3y Where x

Given the cost function (in dollars) C(x, y) = 300 + 2x + 3y. Where x and y represent the number men\'s t-shirts and women\'s t-shirts respectively. Each sells at the price of $12 and $13 respectively. Find the following and interpret, stating the appropriate units: a) Revenue function, R b) Profit function, P C) R_x (100,50) d) P(10,9) - P(9,9)

Solution

x = Number of men\'s t-shirts

y = Number of women\'s t-shirts

(a)
=> Revenue , R(x , y) = 12x + 13y

(b)
=> Profit Function , P(x , y) = R(x , y) - C(x , y)

=> P(x , y) = 12x + 13y - 300 - 2x - 3y = 10x + 10y - 300

(c)
Rx = 12
R(100 , 50) = 12(100) + 13(50) = 1850

(d)
P(10,9) = 100 + 90 - 300 = - 110
P(9,9) = 90 + 90 - 300 = -120
P(10,9) - P(9,9) = (-110) - (-120) = $10