Soru

A boutique catering kitchen prepares custom corporate event packages containing two types of dessert selections: Specialty Layer Cakes ($L$) and Miniature Cupcake Sets ($M$). Each Specialty Layer Cake requires $3$ hours of decorating labor and $4$ kg of specialized flour. Each Miniature Cupcake Set requires $1$ hour of decorating labor and $2$ kg of specialized flour. For an upcoming event order, the kitchen has a maximum resource availability of $30$ total hours of decorating labor and $44$ kg of specialized flour. To meet client specifications, the kitchen must produce at least $4$ Specialty Layer Cakes. If each Specialty Layer Cake yields a profit of $\$50$ and each Miniature Cupcake Set yields a profit of $\$20$, which of the following pairs of $(L, M)$ represents the combination of Specialty Layer Cakes and Miniature Cupcake Sets that maximizes total profit while satisfying all resource constraints?