A dairy is considering expanding their current milk products to include a new orange milk. Currently, the milk is marketed per bottle and the dairy makes white and chocolate milk. Current prices, for the existing milk products are $4.00/bottle for white milk and $4.75/bottle for chocolate milk. White milk costs $2.00/bottle to produce and chocolate milk costs $2.25/bottle. The new orange milk product would retail at $5.25/bottle and cost $2.75/bottle to produce.

Their current creamery capacity limits production to 1,000 bottles per day. The company’s labor budget can employ up to 8 employees to work 8 hours per day. Labor requirements are 0.07, 0.08, and 0.11 man‑hours per unit corresponding to the three bottle lines (white, chocolate, orange), respectively.

1.) Write out the mathematical formulation of the problem.