Please solve and show all work for the following question:

2. A Hungry Student A student has only three things in her cupboard: poptarts, trail mix, and beef jerky. She needs a meal with 1450 calories, 50 grams of fat, and 180 mg of sodium. Per serving, poptarts have 200 calories, 10 grams of fat, and 30 nag of sodium. Per 50-gram serving, trail mix has 150 calories, 5 grams of fat, and 15 mg of sodium. Per IUD-gram serving, beef jerky has 550 calories, 20 grams of fat, and 60 nag of sodium. (a) The student will construct her meal by solving a linear algebra problem, with ':| equations and l variables. Please ll in the blanks and then write the linear system below. Be sure to also clearly dene each variable and indicate what each equation represents. (Use units of servings for food.) (b) What is the augmented matrix for this problem? Please reduce this matrix to Reduced Row Echelon Form. Be sure to label all of your row operations. Hint: the computations to nd the RREF may be much. easier if you exchange certain miss rst. Take a moment to strategize before before you begin. (c) Find a general solution in parametric form. (Please call your parameter t.) In plain English, what does your solution represent in terms of servings of poptarts, 50-gram servings of trail mix, and IOU-gram servings of beef jerky? (d) At the level of solutions to linear algebra problems, the parameter t in your solution can generally take on any value. But in terms of food in the cupboard, it can't, even with a very large supply of all three items in the cupboard. For realistic solutions, what range of values can your parameter take? Why? The parameter must lie in the range ':I g t g |:|. (e) Poptarts cost $1.50 per serving, trail mix costs $2 per serving, and beef jerky costs $8 per serving. i. Using your intuition, can you predict the composition of the cheapest meal and most expensive meal? Discuss this with your pod. (You do not need to record your conversation here.) ii. Find the cost and composition of the cheapest meal, in terms of servings of pop tarts, trail mix and beef jerkey. Hint: Start by nding a formula for the total meal cost as a function of the parameter, C (t) Show your reasoning and state your nal answers below. The cheapest meal would be comprised of servings of poptarts, 50-gram servings of trail mix, and IOU-gram servings of beef jerkey. The cheapest meal costs dollars