A diet is to include at least 140 milligrams of Vitamin A and at least 145 milligrams of Vitamin B. These requirements can be obtained from two types of food. Type X contains 10 milligrams of Vitamin A and 20 milligrams of Vitamin B per pound. Type Y contains 30 milligrams of Vitamin A and 15 milligrams of Vitamin B per pound. If type X food costs $12 per pound and type Y food costs $8 per pound how many pounds of each type of food should be purchased to satisfy the requirements at the minimum cost? Round to the nearest hundredths.

Answer:Food X must not be produced. 9.67 pounds of Food Y should be produced. Step-by-step explanation:To solve this linear programming problem, we can use Solver in Excel, as shown in the attached file. Two decision variables are created: Food X and Food Y. There are two restrictions regarding the amount of vitamin A and B required for each type of Food. The optimal solution is: The minimum optimal cost is $ 77.33 Food X must not be produced. 9.67 pounds of Food Y should be produced.