Wild Nectar Juice bar produces three different smoothies (Energizer, Recovery, and Nightcap) by blending Apple, Orange, Carrot and Strawberry juice. Smoothies are sold in 0.5 litre glasses, and the profit of each glass of Energizer smoothie is $7, each glass of Recovery smoothie is $6, and for each glass of Nightcap is $5. The store manager estimates that on a typical day, they can sell up to 250 glasses of Energizer, up to 200 glasses of Recovery, and up to 300 glasses of Nightcap. However, only 150 litres of each juice is available each day. Energizer and Recovery smoothies are both produced by blending Apple, Orange and Carrot juice. At least 50% of Energizer smoothie and 30% of Recovery should consist of Carrot juice. Moreover, the proportion of unused Apple juice should not be larger than the proportion of unused Orange juice. Finally Nightcap smoothie consists of exactly equal portions of Apple, Carrot, and Strawberry juice. Formulate a linear programming problem that helps the manager to find the best way of combining juices in order to maximize the daily profit of the store. Label your constraints.