# [closed] What products to make, how much to make and in what plants to make them?

 0 A company wants to make 3 new products for the upcoming week. Each product can be made in 1 of 2 plants. At most 2 of the 3 new products should be chosen to be made. Only 1 of the plants should be chosen to make the (0, 1 or 2) products. Below is the Production hours for a unit of product $j$ in plant $i$ total available production hours available for the week the profit/unit and maximum sales/week estimated for product $i$ I have to formulate a linear model that allows to solve for what products to make, how much to make and in what plants to make them so that we can maximise profit. What I tried: Let $x_{ij}$ be hrs spent on making product j in plant i where $i=1,2$ and $j=A,B,C$. Let $y_i$ be $1$ if plant $i$ is chosen and $0$ otherwise. Let $z_j$ be $1$ if product $j$ is made and $0$ otherwise. We want to maximise profit given by $$z = 5000(x_{1A} + x_{2A}) + 7000(x_{1B} + x_{2B}) + 3000(x_{1C} + x_{2C})$$ subject to the constraints: Plant 1 Production Hours $$3x_{1A} + 4x_{1B} + 2x_{1C} \le 30$$ Plant 2 Production Hours $$4x_{2A} + 6x_{2B} + 2x_{2C} \le 40$$ Max Sales for Product A $$x_{1A} + x_{2A} \le 7$$ Max Sales for Product B $$x_{1B} + x_{2B} \le 5$$ Max Sales for Product C $$x_{1C} + x_{2C} \le 9$$ At most one plant $$y_1 + y_2 \le 1$$ If plant $i$ is not chosen then $x_{iA} = x_{iB} = x_{iC} = 0$: $$x_{ij} \le My_i$$ At most two products $$z_A + z_B + z_C \le 2$$ If product $j$ is not made then $x_{1j} = x_{2j} = 0$: $$x_{ij} \le Mz_j$$ Nonnegativity (we can consider fractions of hours) $$x_{ij} \ge 0$$ Binary constraint $$y_i, z_j \in {0,1}$$ Is that right? asked 10 Apr '16, 05:45 BCLC 8●3●12 accept rate: 0% Ehsan ♦ 4.8k●3●11●22 1 Reposting your exam question (https://www.or-exchange.org/questions/13543/how-many-units-of-each-product-should-be-produced) without the picture, so that users will not realize it is an exam question, is obviously a deliberate deception. If you are seeking to be banned from the site, you are on the right track. (11 Apr '16, 15:32) Paul Rubin ♦♦ @PaulRubin What do you mean deliberate deception? Are you accusing me of cheating? I asked my professor about this two days ago on the morning of my make-up exam, and he answered me. If you don't believe me, contact him: bit.ly/ORhandouts (12 Apr '16, 02:05) BCLC After I told you that your question might be homework, you deleted it and reposted it so others could not see my comment. This is what someone might consider to be a deliberate deception. (13 Apr '16, 01:42) Ehsan ♦

### The question has been closed for the following reason "Duplicate Question" by Ehsan 13 Apr '16, 01:42

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