Suppose that a barge (a flat-bottomed boat) needs to pass through a narrow channel between two canals. The channel has half-width W = 10m, maximum depth D = 4m, and a cross-sectional depth described by the function: 3(x) = D(1 - 4) The diagram below (not to scale) shows the situation: 0 surface barge D W y = D y D (1-W) Note that in this diagram down has been taken to be the positive y direction, so that the graph matches up to what a cross-section of the barge would look like with the barge in the channel. Determine the width and depth of the barge that would maximize the cross-sectional area (and hence the mass of the payload) of a fully-loaded barge that could navigate the channel. Verify that these dimensions do, in fact, maximise the cross-sectional area, by checking the value of the second derivative of area. What is the value of the total width of the barge (in metres) that maximises the cross-sectional area? Enter your answer to 2 decimal places, taking care to round appropriately. You do not need to type m at the end to indicate your value is in terms of metres, just enter the numerical value.