its about cost minimization please help me find the solution with clear process
ID: 1129084 • Letter: I
Question
its about cost minimization
please help me find the solution with clear process
thank you
Topic: Cost Minimization % Correct Responses: 55 Correct Answer: D Difficulty: o Discrimination Index: 39 A firm has production function f(ri.z2.73,24)- min(r1,72) +min(z3, z4). This firm faces titive factor markets where the prices for the four factors are wi =6 w2-8, t 3-6 and 20.41 t14 = 3. The firm must use at least 20 units of factor 2. The cost of producing 100 units in the cheapest possible way is: (a) 1,400 (b) 900 (c) 1,160 (d) 1,000 (e) 300Explanation / Answer
Here we have to find out the cost of 100 units in cheapest way so 100 = min (x1, 20)+ min(x3, x4) Since we have to minimize the cost so we do not wat to use more than 20 units of x1 so, 100 = 20 + min (x3, x4) then min (x3, x4) = 80 Now again we to calculate the min cost so we have possible of x3 and x4, that is x3 = x4 = 80 and finally the cost of the production is 20*6 + 20*8 + 80*6 + 80*3 120 + 160 + 480 + 240 = $1000. So our answer is option c
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