Question

Show all your work. In each case, check 2nd order conditions

9) To fill an order for 100 units of a product, a firm wishes to distribute the production between its two plants, Plant 1 and Plant 2. The total cost function is given by 2 c= Kqq, 92) = 0.59 i+2q1+: the number of units produced 3292 and + 500, where are 91 92 at Plants 1 and 2, respectively. How should the output be distributed in order to minimize costs?

Answer 1

Answer-9 - Minimize : c = 0.59, +29, + 32 +500 Subject to q + q = 100 Legrange is given day: ki = 0.59, +29; + 324, +500 + 4(100-4,-22) first dider Condition: da o q + 2 = AV- 2 2 = 0 -> 32 h. = q = 6 - 2 = 32-2 = 30 1 from u => 92 = 100 -- q = 100 - 30.270 Hence In should and 70 order to minimize cost he produce 30 units in plant - 1 units in plant-2. ..

Second Hessian order Condition: is given by : H - 222 1 > H =_to 3+1 => HE 7)*(-160) - (-1)(13) = H = 1(0+) =) >0 Heice There is a Minima. lence above solution q = 30 & q = 70 Satisfies condition of Minuma.