Question

A computer manufacturer produces three types of computers: laptop, desktop, and tablet The manufacturer has designed their supply chain in such a way so that the final assembly of their computers entails putting together different quantities of the same parts. We will assume that the costs for parts unique to the model have already been accounted for in the reported per-unit profits, and that inventory levels for these other parts do not change the optimal allocation. We assume that there are three parts: CPU, RAM, and Hard Drive, each labels, respectively, as part 0, part 1, and part 2. The manufacturer would like to know how many of each model it should manufacture so as to maximize their total profit. However, if inventory of the raw materials is left over after sales within the planning period, then the manufacturer is charged a per-unit fee for each part. Use this information to construct a linear program and to answer the questions below

What is the set of constraints? (a) a0,0x0 + a0,1x1 + a0,2x2 + a0,3x3 + a0,4x4 ≤ b0 a1,0x0 + a1,1x1 + a1,2x2 + a1,3x3 + a1,4x4 ≤ b1 a2,0x0 + a2,1x1 + a2,2x2 + a2,3x3 + a2,4x4 ≤ b2 (b) a0,0x0 + a0,1x1 + a0,2x2 + a0,3x3 ≤ h0 a1,0x0 + a1,1x1 + a1,2x2 + a1,3x3 ≤ h1 a2,0x0 + a2,1x1 + a2,2x2 + a2,3x3 ≤ h2 a3,0x0 + a3,1x1 + a3,2x2 + a3,3x3 ≤ h3 a4,0x0 + a4,1x1 + a4,2x2 + a4,3x3 ≤ h4 (c) a0,0x0 + a0,1x1 + a0,2x2 ≤ b0 a1,0x0 + a1,1x1 + a1,2x2 ≤ b1 a2,0x0 + a2,1x1 + a2,2x2 ≤ b2 a3,0x0 + a3,1x1 + a3,2x2 ≤ b3 (d) a0,0x0 + a0,1x1 + a0,2x2 ≤ h0 a1,0x0 + a1,1x1 + a1,2x2 ≤ h1 a2,0x0 + a2,1x1 + a2,2x2 ≤ h2

Answer 1

We assume that there are three parts: CPU, RAM, and Hard Drive, each labels, respectively, as part 0, part 1, and part 2.

The manufacturer would like to know how many of each model it should manufacture so as to maximize their total profit.

However, if inventory of the raw materials is left over after sales within the planning period, then the manufacturer is charged a per-unit fee for each part.

The manufacturer has designed their supply chain in such a way so that the final assembly of their computers entails putting together different quantities of the same parts.

The set of constraint value is get by the multiplication of the coefficient of the specific part with decision variable.

So d is the correct answer that is

(d) a0,0x0 + a0,1x1 + a0,2x2 ≤ h0 a1,0x0 + a1,1x1 + a1,2x2 ≤ h1 a2,0x0 + a2,1x1 + a2,2x2 ≤ h2.

Here x0, x1, x2 are the decision variables for CPU, RAM and Hard Drive respectively.