Problema Solution
Company hauls gravel to a vconstruction site using a small truck and large truck. Price per load is given. Must deliver a minumum 100 cubic yards per day to satisfy contract with the builder. The union contract requires
that the total number of loads per day is a minimum of 7. How many loasds should be made in each truck per day to minimize the total cost?
Small truck Large truck
Capacity (yd^3) 20 50
Cost per load $70 $63
Answer provided by our tutors
Let x be the small truck and y be the large truck.
20x + 50y >= 100this is the inequality for the amount of gravel
x + y >= 7this is the inequality for the number of loads
C = 70x + 63ythis is the function to be minimized
Graphing both inequalities provides a feasible region with intersection points at (0,7) and (7,0). Plugging each of those points into the function:
(7,0) - cost is $490
(0,7) - cost is $441 - this is the cheaper cost, so the best way to minimize the cost is to move 7 loads with the large truck each day.