c) Since the allowable increase is 333,33 units - the extra 100 units will be 100 times the first unit (the objective function will increase linearly as the capacity increase on engine assembly - till 4333.33). You can re run the model with new numbers plugged in. (please show this)
Determine the critical points of the function: f(x1, x2) = (2 - x1 - x2)^2 + (1 + x1 + x2 - x1*x2)^2. Try to decide their nature.
Check that the function: f(x1, x2, x3) = (x1)^2 + (x2)^2 + (x3)^2 - x1 - x2 - x3 is convex. Find the extreme values of f under the conditions: (x1)^2 + (x2)^2 = 4, -1 <= x3 <= 1. (x3 goes from -1 to 1)
Find the maximum and minimum values of: f(x1, x2) = int(1/(1+t^4), t = x1..x2) over the region determined by (x1)^2 * (x2)^2 = 1 (attached is a .jpg version of the function)
Finding closet point to surface.
Find the closest point of the surface: xy + xz + yz = 1 to the origin. and x^2 + y^2 - Z^2 = 1 to the origin.
Find the length of shortest ladder in the given scenario.
A box of dimensions a x b is standing against a wall that a ladder must lean up against, as shown in the attached picture of the scenario. Formulate the problem of finding the shortest ladder and then solve it.
I have an equation for a ladder leaning up against a box of a x b that is against a wall. The equation is: L(m) = (a - (b/m)) * SQRT(1 + m^2) I need to find the optimal m value to minimize L(m).
Minimizing cost of laying cable... (Please see the attachment).
A factory is located on one bank of a stratight river that is ... (Please see the attachment).
Each machine at a certain factory can produce 50 units per hour. The setup cost is $80 per machine, and the operating cost is $5 per hour. How many machines should be used to produce 8,000 units at the least possible cost? (Remember that the answer should be a whole number.)
Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and four sides of the box costs $1/ft^2; the material for the base costs $2/ft^2. FInd the dimensions of the box of greatest possible volume if you are allowed to spend $144 for the material to make it.
