Suppose that for example 15.1, the gas-processing plant decides to produce a third grade of product with the following characteristics: supreme raw gas 15 m3/tonne production time 12 hr/tonne storage 5 tonnes profi t $250/tonne in addition, suppose that a new source of raw gas has been discovered so that the total available is doubled to 154 m3/week.

(a) set up the linear programming problem to maximize profi t.
(b) solve the linear programming problem with the simplex method.
(c) solve the problem with a software package.
(d) evaluate which of the following options will raise profi ts the most: increasing raw material, storage, or production time.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles