A diet-conscious housewife wishes to ensure her family’ daily intake of vitamins A, B and C does not fall below the following levels, 24 units for vitamin A, 23 units for vitamin B, and 25 units for vitamin C. For this she relies on two fresh foods. One ounce of the first food provides 8 units of vitamin A, 6 units of vitamin B, and 4 units of vitamin C. One ounce of the second food provides 3 units of vitamin A, 5 units of vitamin B, and 7 units of vitamin C. If the first food costs 3 pence per ounce and the second food costs 2 pence per ounce, find how many ounces of each food should be bought by the housewife daily in order to keep her food bill as low as possible. (1) Formulate the problem as a linear programming problem. (2) Solve this linear programming problem graphically. (3) Perform the first step of solving the linear programming problem using Simplex method. (i) Transfer the problem into the Standard Format by introducing slack variables; (ii) In the graph you drew, point out which points are Basic solutions and which points are Basic feasible solutions. How many Basic solutions and how many Basic feasible solutions are there?
A diet-conscious housewife wishes to ensure her family’ daily intake of vitamins A, B and C does not
fall below the following levels, 24 units for vitamin A, 23 units for vitamin B, and 25 units for vitamin C.
For this she relies on two fresh foods. One ounce of the first food provides 8 units of vitamin A, 6 units
of vitamin B, and 4 units of vitamin C. One ounce of the second food provides 3 units of vitamin A, 5
units of vitamin B, and 7 units of vitamin C. If the first food costs 3 pence per ounce and the second food
costs 2 pence per ounce, find how many ounces of each food should be bought by the housewife daily in
order to keep her food bill as low as possible.
(1) Formulate the problem as a linear programming problem.
(2) Solve this linear programming problem graphically.
(3) Perform the first step of solving the linear programming problem using Simplex method. (i)
Transfer the problem into the Standard Format by introducing slack variables; (ii) In the graph
you drew, point out which points are Basic solutions and which points are Basic feasible
solutions. How many Basic solutions and how many Basic feasible solutions are there?
（If this is the case, please clearly state which part is completed by MATLAB and/or Excel, and how.）
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