# Math Help - minimization problem

1. ## minimization problem

You must deliever a min. of 200 cubic yards per day to satisfy a union contract. The union contract requires that the total number of loads per day is a min. of 6. How many loads should be made in each truck per day to minimize the total cost?

Small Truck Large Truck
Capacity (yd^3) 40 60

Cost per Load $61$43

2. Originally Posted by cobragrrll
You must deliever a min. of 200 cubic yards per day to satisfy a union contract. The union contract requires that the total number of loads per day is a min. of 6. How many loads should be made in each truck per day to minimize the total cost?

Small Truck Large Truck
Capacity (yd^3) 40 60

Cost per Load $61$43

per day for a cost of $258. RonL 3. Originally Posted by cobragrrll You must deliever a min. of 200 cubic yards per day to satisfy a union contract. The union contract requires that the total number of loads per day is a min. of 6. How many loads should be made in each truck per day to minimize the total cost? Small Truck Large Truck Capacity (yd^3) 40 60 Cost per Load$61 $43 Umm, another linear programming, as I see it. Decision variables: s = number of small truck to use per day L = number of Large truck to use per day. Problem constraints: Per minimum required volume per day, 40s +60L >= 200 2s +3L >= 10 ------------(1) Per minimum required number of number of loads per day, s +L >= 6 -----------(2) The problem did not specify that both small and large trucks must be used. Just minimum of 6 loads---using whatever trucks, apparently. Non-negative constraints, s >= 0 ------------------------(3) L >= 0 ---------------(4) Objective function: To minimize cost. Total Cost, C = s*$61 +L*$43 C = 61s +43L -------in dollars. Using rectangular s,L axes, where horizontal axis is for values of s, and vertical axis is for values of L, graph the 4 linear inequalities above. Find the corner points of the feasible region. You should arrive at: >>>feasible region is not fully bounded. Its only boundaries are the s and L axes, and the linear inequality (2), and then it is open up to before positive infinity. Although inqualities (1) and (2) intersect at (8,-2), this point is not a corner point of the feasible region because consntraint/inequality (4) says L >=0. >>>Corner points are (0,6) and (6,0) only. Test objective function on those corner points, ---at (0,6), C = 61*0 +43*6 =$258.