Question $2(5$ points$)$

Wild Nectar Juice bar produces three different smoothies $($Energizer$,$ Recovery, and

Nightcap$)$ by blending Apple, Orange, Carrot and Strawberry juice.

Smoothies are sold in $0\mathrm{.}5$ 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.

Either type your answer or attach a high quality photo of your handwritten response.