This question tests the student's ability to model and solve Integer Programming problems
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"prompt": "P-{c36}{a32}{s75}: You are in charge of renting Suburbans and vans for your family reunion. You know that at least {c361} children (all 7 years old and younger) are attending and that at least {a321} adults (the rest that have not confirmed have no children) are attending. Each Suburban accommodates {sc61} children, {sa41} adults and costs {s751} \\$ to rent. Each van accommodates {vc41} children, {va41} adults and costs {v1001} \\$ to rent.
\nSet-up the linear programming problem using variables x1, x2, ...
\nA. Objective:[[0]] [[1]]
\n
B. Give the system of constraints:
for children: [[2]]$\\ge$[[9]]
\nfor adults: [[3]]$\\ge$[[10]]
\n\nC. Range of varables:
\n$x_1$ is [[4]]
\n$x_2$ is [[5]]
\n
D. How many Suburbans and vans should be
rented to minimize cost?
Suburbans: [[6]], Vans: [[7]]
\n
E. What is the minimum cost? [[8]]
This question tests the student's ability to model and solve Integer Programming problems
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\nFormulate the linear programming problem using variables x1 (for $x_1$ Pill I), ...
\nPut \">=\" for \"$\\ge$\" and \"<=\" for \"$\\le$\".
\n\nA. Objective:[[0]] [[1]]
\n
B. Give the system of constraints:
for vitamin A: [[2]]$\\ge$[[10]]
\nfor potassium: [[3]]$\\ge$[[11]]
\nfor beta carotene [[4]]$\\ge$[[12]]
\n\nC. Range of varables:
\n$x_1$ is [[5]]
\n$x_2$ is [[6]]
\nD. Optimal solution: $x_1$ = [[7]], $x_1$ = [[8]]
\nE. Minimal cost: [[9]]
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\nFormulate the linear programming problem using variables x1 (for $x_1$ Plan I), ...
\nPut \">=\" for \"$\\ge$\" and \"<=\" for \"$\\le$\".
\n\nA. Objective:[[0]] [[1]]
\n
B. Give the system of constraints:
for carbohydrates: [[2]]$\\ge$[[9]]
\nfor protein: [[3]]$\\le$[[10]]
\n\nC. Range of varables:
\n$x_1$ is [[4]]
\n$x_2$ is[[5]]
\nD. Optimal solution: $x_1=$ [[6]], $x_2=$ [[7]]
\nE. The minimum number of grams of fat taken in per day is [[8]]
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\nBrand 2: {bv4} units of vitamin A, {bb2} units of biotin and {bs3} units of sodium.
\nThe amount of sodium in their diet must be minimized. Formulate the linear programming problem using variables x1 (for $x_1$ Brand 1 pills), ...
\nPut \">=\" for \"$\\ge$\" and \"<=\" for \"$\\le$\".
\n\nA. Objective:[[0]] [[1]]
\n
B. Give the system of constraints:
for vitamin A: [[2]]$\\ge$[[9]]
\nfor biotin: [[3]]$\\ge$[[10]]
\n\nC. Range of varables:
\n$x_1$ is [[4]]
\n$x_2$ is[[5]]
\nD. Optimal number of pills: Brand 1 $x_1$ = [[6]], Brand 2: $x_1$ = [[7]]
\nE. The minimum sodium intake is [[8]]
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\nMaximize: $\\simplify{{kx} x + {ky} y}$
\nSubject to
\n$ \\simplify{{k5} x - y} \\ge \\var{k6}$
\n$ \\simplify{100*{k2} x + 100*{k1} y} \\le \\var{100*s}$
\n$ \\simplify{100*{k22} x + 100*{k11}y} \\le \\var{100*ss} $
\n$ \\simplify{{k7} x - {k8} y} \\le \\var{sss}$
\n$x,y \\ge 0$
\n\nOptimal solution: $x=$[[0]], $y=$[[1]]
\nMinimum function value: [[2]]
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