DO NOT USE ANY APP OR SOFTWARE TO SOLVE THE PROBLEM ( LINGO, ETC )

Fruit Computer Company is ready to make its annual purchase of computer chips. Fruit can purchase chips (in lots of 100) from three suppliers. Each chip is rated as being of excellent, good, or mediocre quality. During the coming year, Fruit will need 5,000 excellent chips, 3,000 good chips, and 1,000 mediocre chips. The characteristics of the chips purchased from each supplier are shown in Table 57.

Each year, Fruit has budgeted $28,000 to spend on chips. If Fruit does not obtain enough chips of a given quality, then the company may special-order additional chips at $10 per excellent chip, $6 perbgood chip, and $4 per mediocre chip. Fruit assesses a penalty of $1 for each dollar by which the amount paid to suppliers 13 exceeds the annual budget. Formulate an LP to help Fruit minimize the penalty associated with meeting the annual chip requirements. You must write down the characteristics of the following Goal Programming problem clearly and completely, namely Decision Variables, Deviational Variables, Objective Function, Constraint, and Sign Restriction.

TABLE 57 Characteristics of a Lot of 100 Chips Supplier Excellent Good Mediocre 1 60 20 20 2 50 35 15 3 20 40 Price Per 100 Chips (8) 400 300 250 40