Supersport footballs, inc. has the problem of determining the best number of allpro(x1), college(x2), and high school(x3) models of footballs to produce in order to maximize profits. the profits of producing one allpro football, one college football, and one high school football are respectively $3, $5, and $4. constraints included production capacity limitations in each of three departments (cutting and dyeing, sewing, and inspection and packaging) as well as the constraint for at least 1000 allpro footballs. the linear program formulation is shown below and the corresponding solver solution and sensitivity analysis output is below. max 3x1 + 5x2 + 4x3 s. t. (time in minutes) 12x1 + 10x2 + 8x3 ? 18,000 (cutting and dyeing) 15x1 + 15x2 + 12x3 ? 18,000 (sewing) 3x1 + 4x2 + 2x3 ? 9,000 (inspection and packaging) x1 ? 1,000 (allpro model) x1, x2, x3 ? 0using the solver information below answer the following questions: (a) how much slack time is available in each of the three production departments? include the proper time units.