How much of each food itemwould maximize the value of nutrient 3

2. Solve by Lagrange Multiplier Method: Clearly identify your constraint function and your system. You may use either approach you learned in class and on the video. Mr. Eppolito has S360 to spend on fencing to fence a rectangular garden. The fencing for the north and south sides of the garden costs $10/ft. The fencing for the east and west sides costs $15/ft. Find the dimensions that will allow Mr. Eppolito to fence in the largest-sized garden. Draw a diagram of this scenario. Write the method you will use to solve it, then do so, showing all the necessary equations.

Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard model requires 5 hours to assemble and 1 hours for finishing touches. The artisan model requires 2 hours to assemble and 4 hours for finishing touches. Based on their current staffing, they can manage a maximum number of assembly hours available is 50 per day, and the maximum number of finishing hours available is 64 per day. Let x = the number of standard model bookcases produced per day and y = the number of artisan model bookcases produced per day. Write the system of inequalities that represents the maximum number of bookcases that can be produced in one day. 0 Graph the system of inequalities, remember to include x >0 and y > 0 in your graph to get full credit. You will need to include four lines. 25 24 VI

Yang's Material Company hauls gravel to a construction site, using a small truck and a large truck. The carrying capacity and operating cost per load are given in the accompanying table. Yang must deliver a minimum of 120 cubic yards per day to satisfy his contract with the builder. The union contract with his drivers requires that the total number of loads per day is a minimum of 5. How many loads should be made in each truck per day to minimize the total cost? Capacity (yd³) Cost per Load Small Truck Large Truck 40 30 $90 $72 In order to minimize the total cost, the number of loads in a small truck that should be made is be made is. and the number of loads in a large truck that should