Need help with this LP problem The Food Max grocery store sells three brands of

Question

Need help with this LP problem

The Food Max grocery store sells three brands of milk in half-gallon cartons – its own brand, a local dairy brand, and a national brand. The profit from its own brand is $0.97 per carton, the profit from the local dairy is $0.83 per carton, and the profit from the national brand is $0.69 per carton. The total refrigerated shelf space allotted to half-gallon cartons of milk is 36 square feet per week. Each milk carton takes up 12 square inches of space. Food Max always sells more of the national brand than of the local dairy brand and its own brand combined and at least three times as much of the national brand as its own brand. In addition the local dairy can only supply 10 dozen cartons per week. The store manager wants to know how many half-gallon cartons of each brand to stock each week in order to maximize profit.

Formulate the problem using the following steps.

a. Define the decision variables.

b. Specify the objective function.

c. Specify the constraints and simplify them so that the left hand side of each constraint only contains terms involving the decision variables.

Thanks

Explanation / Answer

(a) The decision variables:

i. The number of half-gallon cartons of own brand: O

ii. The number of half-gallon cartons of local brand: L

iii. The number of half-gallon cartons of national brand: N

(b). The objective function, Maximize 0.97O + 0.83L + 0.69N

(c) Constraints:

i. 12(O + L + N) <= 36*12*12 [space constraint] => O+L+N <= 432

ii. N > O+L [national brand is more sold than own and local combined] => N-O-L > 0

iii. N > 3O [national brand sold more than thrice own] => N-3O > 0

iv. L <= 10*12 [local dairy provides 10 dozens per week] => L <= 120

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