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Faculty of Engineering
ME30B
Assignment 1 (Additional)
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]