The Department of the Navy has been downsizing and is looking for cost savings opportunities to meet mandated congressional budget cuts. One suggestion under consideration is to change the make up of content of Navy sea rations, the canned food supplies containing certain minimum quantities of Vitamin A, Vitamin D, iron, and other nutrients, which combat troops carry into battle.
According to Texfoods, the current supplier of sea rations for the Navy, each two-ounce portion of its product supplies 20% of the required amount of Vitamin A, 25% of the required amount of Vitamin D, and 50% of the required amount of iron. Each portion costs the Navy $.60. Because all minimum standards must be met in each serving, the current sea ration container must contain 10 ounces of the Texfoods product (to meet the minimum amount of Vitamin A). This costs the Navy $3.00 (=5 * $.60) per serving.
The Navy is considering switching to another product from a different supplier, Calration. A two-ounce portion of Calration costs $.50 and provides 50% of the minimum requirement of Vitamin A and 25% of the requirement of Vitamin D, but only 10% of the requirement for iron. Substituting the Calration product, the sea ration container would have to contain 20 ounces in order to meet the minimum iron requirement, costing the Navy $5.00 (=10 * $.50) per serving.
One bright lieutenant has suggested that a mixture of the two products might meet the overall standards at a lower cost than the current $3 per serving. The Navy has never worried about the taste of sea rations; hence, mixing them, either by combining them or by packing a portion of each, is an acceptable alternative. The lieutenant has been given permission to evaluate the idea. Considering the problem posed by the lieutenant, provide an optimal solution that complies with the following three conditions:
1. Determine the amount of two-ounce portions of each sea ration product in the mix.
2. Minimize the total cost of the sea rations.
3. Meet the minimum requirements for Vitamin A, Vitamin D, and Iron. Should the cost per 2 oz. portion of the Calration product increase to $.75,
4. Would the optimal product mix change? If the cost per 2 oz. portion of the Texfoods product increases to $1.05 while the cost per 2 oz. portion of the Calration product decreases to $.30,
5. Would the optimal product mix change?