Question

Jane is selling apple and oranges she has to first buy the fruit from the grocery store and pays $2 per apple and $3 per orange and only has $18 to spend. Together she can sell a maximum of 12 pieces of fruit. Show all the possible combinations of fruit she can sell. Then list two possible combinations

Answer 1

To find all possible combinations of apples and oranges Jane can sell, we use the budget constraint (2A + 3O <= 18) and the quantity constraint (A + O <= 12). By systematically varying the number of apples and calculating the corresponding number of oranges within her budget, we can list the combinations. Two such combinations are 3 apples with 4 oranges, and 6 apples with 2 oranges.

Step-by-step explanation:

Jane wants to determine all possible combinations of apples and oranges she can sell while not exceeding her budget of $18 and being limited to selling at most 12 pieces of fruit. To find these combinations, we set up two equations based on the given information:

2A + 3O ≤ 18 (Budget constraint, where A is the number of apples and O is the number of oranges)

A + O ≤ 12 (Quantity constraint)

By iterating through possible quantities of apples (A) and calculating the maximum number of oranges (O) that can be bought with the remaining budget, we can list all possible combinations. For example, if Jane buys 0 apples, she can spend all $18 on oranges, buying 6 oranges (since $18 ÷ $3 per orange = 6 oranges). If she buys 1 apple for $2, she has $16 left for oranges and can buy 5 oranges with that amount ($16 ÷ $3 per orange = 5 + 1/3, rounded down to 5). We would continue to list out combinations until the quantity constraint or the budget constraint is violated.

Two possible combinations that Jane could sell are:

3 apples and 4 oranges (costing 3*$2 + 4*$3 = $18 and summing to 7 pieces of fruit)

6 apples and 2 oranges (costing 6*$2 + 2*$3 = $18 and summing to 8 pieces of fruit)