Please help me with part a, b and c

Valu-Com Electronics manufactures different models of telecommunications interface cards for PCs and laptops. Valu-Com Electronics has been nancially prosperous during its rst few months of operation and is already considering the possible relocation and product expansion within the year to a facility in Penang, Malaysia, where both material and labour costs are noticeably lower. The availability of cheaper labour and a contract with a local distributor to supply up to 3000 sets of materials at a substantially reduced cost will effectively double the prot for Hyper-Links $16 per batch and triple the prot for FastLinks to $15 per batch. The new facility will be equipped with machinery and staffed with workers to facilitate a 40-hour regular time work schedule. Moreover, up to 32 hours of overtime can be scheduled. Considering the benets, wages, and other plant operating expenses, each scheduled overtime hour will cost the company 3180 more than regular time hours. Valu-Com has been testing marketing two additional products, tentatively named the MicroLink and the EtherLink, which appear to be as popular as the Hyperlink and FastLink. Table 1 shows the prot and requirements for each product line. Valu-Com has a signed contract with Castle IT to supply it with 200 batches of FastLinks monthly once the relocation has taken place. The marketing department has revised its strategy for the post- relocation period. It has concluded that to keep total demand at its peak, Valu-Com's most popular model, the HyperLink, should account for precisely 50% of total production, while no other product line should account for more than 40%. However, instead of limiting production to at most 700 batches monthly, the department wishes to ensure that production will total at least 1000 batch units monthly. An analyst would like to determine the monthly production schedule (including overtime hours, if necessary) to maximise its net monthly prot. Table 1. Prot and requirements per batch Product Prot Materials Production time (min) number of sets H '- erLinks $16 2 3 Fa stLinks $1 5 1 4 MicroLinks $20 3 5 EtherLinks $22. 4 6 Available 3000 40 hrs. re . time 32 rs. overtime (a) Provide a brief specication for your model. It should include an introduction, assumptions, decision variables, objective function, and constraints. [4 marks] (b) Construct the dual model for the primal model formulated in part (a). Identify whether primal and dual models are sensible models. Justify your answer. [2 marks] (c) Implement your model in Excel spreadsheet and R software for the problem formulated in part (a). Compare the results from two software. Find the optimal solutions and optimal objective function value. Discuss the answer and sensitivity reports. [3 marks]