The EK Coffee Shop is planning to make two coffee blends to be sold in the next week: Special and Regular. It uses three different types of coffee to produce the blends: Brazilian, Colombian, and mocha. The shop has the following blend recipe requirements:

Blend	Mix Requirements	Selling Price Per Pound
Special	At least 40% Colombian. At least 30% mocha	$10
Regular	At least 50% Brazilian. Two parts mochas to one part Colombian	$8

The cost of Brazilian coffee is $2 per pound, the cost of Colombian is $4 per pound, and the cost of mocha is $3 per pound. The shop has 100 pounds of Brazilian coffee, 80 pounds of Colombian, and 70 pounds of mocha. The shop wants to make at least 120 pounds of Special blend. Assume that anything that they make can be sold in the next week. The shop needs to decide the amount of each blend it should prepare for the next week to maximize their net profit. ( Include the mathematical formulations and all the descriptions to explain your variables and all necessary constraints including non negativity) Assume: SB,RB is Brazilian pound for Special and Regular; SC, RC are Colombian pound for Special and Regular; SM, RM is Mocha pound for Special and Regular blend

1. Formulate the following problem as a linear programming model. Clearly label all Decision variables, objective function and necessary constrains and equations.
2. Using Python solve the optimizations model and give the following results:
3. Objective Function Value: ______________________
4. Decision Variables Values: __________________________
5. Slack in each constraint :_______________________________