3) Multivariable Calculus Maximizing profit. The market research department for a drugstore chain chose two summer resort areas to test market a new sunscreen lotion packaged in 4-ounce plastic bottles. After a summer of varying the selling price and recording the monthly demand, the research department arrived at the following demand table, where y is the number of bottles pur- chased per month (in thousands) at x dollars per bottle: 5.0 2.0 5.5 1.8 6.0 14 6.5 1.2 7.0 1.1 (A) Use the method of least squares to find a demand equation. (B) If each bottle of sunscreen costs the drugstore chain $4. how should the sunscreen be priced to achieve a maximum monthly profit? [Hint: Use the result of part (A), with C = 4y, R = xy, and P = R - C.] *Hint your demand equation should be in the form y = ax + b(A) Use the method of least squares to find a demand equation. (B) If each bottle of sunscreen costs the drugstore chain $4. how should the sunscreen be priced to achieve a maximum monthly profit? [Hint: Use the result of part (A), with C = 4y, R = xy, and P = R - C.] *Hint your demand equation should be in the form y = ax + b * -1 k-1 n IM M a (10 + 10 marks) k =1 b =