Shipping Carpets: A manufacturer of nylon carpets produces rolls of carpeting at four factories and ships them to distributors in five locations. The table below shows the capacities at the factories and the demands at the distributors for the next quarter, all given in thousands of rolls. Also shown are the unit transportation costs between each factory and each distributor, stated in cost per roll. D1 D2 D3 D4 D5 Copocigr F1 42 F2 F1 F3 53 F4 52 Demand 4-1 56 29 31 59 [a] 10 points: If the manufacturer wishes to meet the demand at the minimum total transportation cost, what is the optimal distribution plan and its cost? [b] 10 points: Suppose that the manufacturer's policy is that each distributor must be supplied from a single factory. What is the optimal distribution plan under this policy