University of the West Indies

Faculty of Engineering

ME30B

Date of Submission: 23rd April, 2004 (or earlier - submit to Evie)

Peg and Al Fundy have two vitamin health foods for sale. Food 1 sells for \$4 per ounce, and each ounce contains 3 units of vitamin A and 1 unit of Vitamin C. Food 2 sells for \$2 per ounce, and each ounce contains 1 unit of each vitamin. Peg and Al want to sell a package whereby a person buying a combination of their health foods have between 3 to 12 units of vitamin A and 4 to 6 units of vitamin C.

a) Formulate a LP model to maximize Peg and Al Fundy sales revenue.                                                                             [3]

b) Solve the problem graphically (using graph paper)                                                                                                         [5]

c) Perform a sensitivity analysis:

(i) Ranges of coefficients                                                                                                                           [2]

(ii) Ranges of RHS                                                                                                                                    [4]

(iii) Dual prices/ shadow prices                                                                                                                  [4]

d) If the maximum required units of Vitamin A are raised to 14, what will be Peg and Al Fundy new sales revenue?                                                                                                                                                                          [1]

e)  If the cost of production of Food 1 and Food 2 is \$2 and \$1 respectively, based on your solution, what will be their profit?                                                                                                                                                                              [1]

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