Optimization problem:

Problem 2. The trendy Italian company Caff d'Oro is a large retailer of packaged premium coffee beans exported from South America. There are 3 different grades of coffee beans used in different products of Caff d'Oro, where grade 1 is of the highest quality and grade 3 is of the lowest quality. Caff d'Oro is facing an enormous demand, and for the upcoming months, they have estimated their bean needs (in pounds (lbs) of coffee beans) for each grade level as follows: Caff d'Oro can purchase from five main suppliers of coffee beans in South America, each of which provides beans in bulk. Caff d'Oro then processes the beans further by separating them according to their grade levels for further use in their retail products. Caff d'Oro has visited the suppliers' facilities and obtained samples to determine the grade level composition (i.e., the fraction of each grade level in the overall content) of each supplier. The table below indicates these results as well as the price per lb of coffee beans for each supplier. Cost (in \$ per lb) and content composition (in fractions) of each supplier. For example, based on the data from this table, if Caff d'Oro orders 100 lbs of coffee beans from Supplier 1, Caff d'Oro will pay $235,000 and will receive 4lbs of grade 1 beans, 42 lbs of grade 2 beans, and 54 lbs of grade 3 beans from Supplier 1 . Caff d'Oro wants to determine how many pounds (lbs) to purchase from each supplier in order to meet its needs for different grade levels of coffee beans, with minimum total cost. We will formulate this problem as a linear program using the following variables: x1 : the amount purchased from supplier 1 (in lbs), x2 : the amount purchased from supplier 2 (in lbs), x3 : the amount purchased from supplier 3 (in lbs), x4 : the amount purchased from supplier 4 (in lbs), x5 : the amount purchased from supplier 5 (in lbs). 5. Write down the objective function. 6. Write down the constraints that ensure we meet the need for coffee beans in each grade level. 7. Implement and solve your LP model in Excel and generate the Answer Report. For your convenience, the data is provided in the spreadsheet problem_set1_S23PT.xlsx. (Remember to solve your model as an LP by selecting Simplex LP as the Solver engine.) 8. What is the optimal objective value? (Round your answers to the nearest three decimal places.) Coffee Supply \begin{tabular}{|l|r|r|r|r|r|} \hline & Cost (\$ per lb) & Grade 1 & Grade 2 & Grade 3 & Amount (Ibs) \\ \hline Supplier 1 & 2350 & 0.04 & 0.42 & 0.54 & \\ \hline Supplier 2 & 2100 & 0.19 & 0.38 & 0.43 \\ Supplier 3 & 2060 & 0.26 & 0.59 & 0.15 \\ Supplier 4 & 1950 & 0.17 & 0.56 & 0.27 \\ Supplier 5 & 1870 & 0.12 & 0.52 & 0.36 \\ \hline & & & & \\ \hline \multirow{3}{*}{ Total cost } & & >= & >= & >= \\ \hline & \multicolumn{2}{|c|}{ Demand (lbs) } & 120 & 180 & 150 \\ \hline \end{tabular}