# Include discount in LP

I'm confused by the question and the second constraint the question probably refers to. There's a production planning model for three fabrics which should maximize profit:

$$max 5x_1 + 12x_2 + 4x_3$$

$$s.t. 1x_1 + 2x_2 + 1x_3 \leq 5$$

$$2x_1 - x_2 + 3x_3 \geq 2$$

in which variables x1, x2 and x3 represent the production levels of fabric A, B and C, where the first constraint is associated with cotton assumption in tons per 1000 meters of produced fabric and the second constraint is related to market demand. The problem statement: Admit that by purchasing more than 5 tons of cotton the company obtains a discount of 1.16 monetary units per ton. What is the new production plan if the profit per unit of each fabric is not changed?

I feel like the first constraint should therefore have a swapped sign. But what about the second constraint? Both as lower bounds seems very strange. A hint would be great. Thanks

• Sorry I forgot the non-negativity constraints – steph Jun 14 '17 at 8:50
• It would be better if you explain more about the constraints. And also how the variables are defined ? – callculus Jun 14 '17 at 9:30
• Yes, you're right. I included in the original words. That's unfortunately all I have. One note because of "new production plan": It is the question number e) and there were plan to compute before. – steph Jun 14 '17 at 9:56
• Unfortunately I have to go now. But I will be back in about 6 hours. – callculus Jun 14 '17 at 9:58
• One question for clarification: Are you allowed to use binary variables ? – callculus Jun 14 '17 at 10:01