1. **Problem statement:** We have 120 mangoes and 180 papayas. We want to make two types of packages. Type A contains 3 mangoes and 3 papayas and sells for 6 each. Type B contains 2 mangoes and 4 papayas and sells for 5 each. We want to maximize profit from sales. 2. **Variables of decision:** Let $x$ be the number of type A packages and $y$ be the number of type B packages. 3. **Constraints:** - Mangoes used: $3x + 2y \leq 120$ - Papayas used: $3x + 4y \leq 180$ - Non-negativity: $x \geq 0$, $y \geq 0$ 4. **Objective function:** Maximize profit $f(x,y) = 6x + 5y$ 5. **Explanation:** The constraints ensure we do not exceed the available fruits. The objective function sums the revenue from each package type. 6. **Answer to part c:** The correct function is $f(x,y) = 6x + 5y$ (option iii). Final answers: - a) Variables: $x$, $y$ - b) Constraints: $3x + 2y \leq 120$, $3x + 4y \leq 180$, $x,y \geq 0$ - c) Objective function: $f(x,y) = 6x + 5y$