Vegetables are primary foods to feed family healthfully

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Reference no: EM132227632

A dietician believes that fish and vegetables are the primary foods to feed her family “healthfully” for the next week. She concludes that at least 30 vitamin units and 16 mineral units altogether from both foods are required to orchestrate a “healthful” approach. In fact, she reasons that each gram of fish contains four vitamin units and one mineral unit, while each gram of vegetables contains three vitamin units and two mineral units. Understandably she wants to minimize the associated cost per week. She estimates that one gram of fish costs $.36 and a gram of vegetables costs $.27.

(a) Record below the linear program that minimizes weekly cost.

(b) Solve the program using the iso-cost approach. What is the optimal dietary mix of fish and vegetables? What is the dietician’s cost that realizes this mix? Explain if the vitamin and mineral requirements have been exceeded at optimality

(c) Find the shadow price for minerals, that is, by how much the value of the program changes if the mineral requirement were increased by one unit. Is this a “good” change or a “bad” change if the dietician were focused on feeding her family even more healthfully? Explain briefly your reply.

Reference no: EM132227632

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