Final answer:
The optimal production mix of rain jackets and rain pants is determined by calculating the maximum number of each product that can be produced while satisfying minimum demand and maximizing contribution margin per minute of machine time, with rain pants being more profitable and thus preferable to produce with available machine time.
Step-by-step explanation:
To determine the optimal production mix of rain jackets and rain pants, we need to calculate the maximum number of each product that can be produced given the constraints of machine hours and minimum demand.
We are given that there are 4,800 hours available on the cutting machine, which translates to 288,000 minutes (4,800 hours x 60 minutes per hour).
Rain jackets take 15 minutes each, and rain pants take 24 minutes each on the cutting machine. To meet the minimum demand of 3,000 units for each product, we must reserve 45,000 minutes for jackets (3,000 units x 15 minutes per unit) and 72,000 minutes for pants (3,000 units x 24 minutes per unit).
After meeting the minimum demand, we have 171,000 minutes left (288,000 - 45,000 - 72,000). To maximize profit, we can further allocate these remaining minutes based on the contribution margin per minute of machine time for each product.
Rain jackets have a contribution margin of $16 for 15 minutes or $1.067 per minute. Rain pants have a contribution margin of $32 for 24 minutes, or $1.333 per minute, making the rain pants more profitable per minute of machine time. Ideally, the company should use the remaining 171,000 minutes to produce as many additional rainpants as possible, given the higher contribution margin per minute.
However, the precise allocation may also depend on market demand, capacity constraints, and other factors.