Johnson's Household Products has a division that produces two types of toothpaste: a regular toothpaste and a whitening tooth paste. The demand equations that relate the prices, p and q (in dollars per thousand units), to the quantities demanded weekly, x and y (in units of a thousand), of the regular toothpaste and the whitening toothpaste are given by p=3000-20 x-10 yp=3000−20x−10y and q=4000-10 x-30 yq=4000−10x−30y respectively. The fixed cost attributed to the division is $20,000/week, and the cost for producing 1000 tubes of regular and 1000 tubes of whitening toothpaste is$400 and $500, respectively. a. What is the weekly total revenue function R(x, y)? b. What is the weekly total cost function C(x, y)? c. What is the weekly profit function P(x, y)?
Johnson's Household Products has a division that produces two types of toothpaste: a regular toothpaste and a whitening tooth paste. The demand equations that relate the prices, p and q (in dollars per thousand units), to the quantities demanded weekly, x and y (in units of a thousand), of the regular toothpaste and the whitening toothpaste are given by p=3000-20 x-10 yp=3000−20x−10y and q=4000-10 x-30 yq=4000−10x−30y respectively. The fixed cost attributed to the division is $20,000/week, and the cost for producing 1000 tubes of regular and 1000 tubes of whitening toothpaste is$400 and $500, respectively. a. What is the weekly total revenue function R(x, y)? b. What is the weekly total cost function C(x, y)? c. What is the weekly profit function P(x, y)? d. How many tubes of regular and whitening toothpaste should be produced weekly to maximize the division's profit? What is the maximum weekly profit?
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