Final answer:
To maximize the annual interest earned, $23,100 should be invested in Stock Boll and the full buying limit of $12,900 in Stock Coff. This allocation will yield the highest possible annual interest of $1,671, given the conditions specified.
Step-by-step explanation:
To maximize the annual interest earned from investing $36,000 in Stock Boll and Stock Coff, we need to determine the amount to invest in each stock while adhering to the given conditions. Stock Coff has a buying limit of $12,900, and we want to invest at least four times that amount in Stock Boll.
First, let's denote the amount to invest in Stock Coff as C. According to the conditions, the maximum amount we can invest in Stock Coff is $12,900. Therefore, C must be less than or equal to $12,900.
For Stock Boll, the amount B to be invested must be at least four times the amount in Stock Coff. This gives us the inequality B ≥ 4C. Since the total investment is $36,000, we also have B + C = $36,000.
To maximize the annual interest, we should fully utilize the buying limit of Stock Coff, since it has a lower interest rate compared to Stock Boll. This means we set C = $12,900. By substitution, B = $36,000 - C = $36,000 - $12,900 = $23,100 for Stock Boll.
Now, calculate the total annual interest: Stock Boll earns 5% and Stock Coff earns 4%. Therefore, the total annual interest is:
(0.05 × $23,100) + (0.04 × $12,900) = $1,155 + $516 = $1,671.
You will earn a maximum total annual interest of $1,671 if you invest $23,100 in Stock Boll and $12,900 in Stock Coff.