MMLU-Pro / 169 / A tomato cannery has 5000 pounds of grade A tomatoes and 10,000 pounds of grade…

A tomato cannery has 5000 pounds of grade A tomatoes and 10,000 pounds of grade B tomatoes, from which they will, make whole canned tomatoes and tomato paste. Whole tomatoes must be composed of at least 80 percent grade A tomatoes, whereas tomato paste must be made with at least 10 percent grade A tomatoes. Whole tomatoes sell for 0.08perpoundandpastesellsfor0.05 per pound. Formulate a linear program to solve for how much of each product to make, if the company wants to maximize revenue. (Hint: Let x_WA = pounds of A grade tomatoes used in whole tomatoes, x_WB = pounds of B grade tomatoes used in whole tomatoes; the amount of whole tomatoes produced can be found as x_WA + x_WB after x_WA and x_WB are chosen.)

A tomato cannery has 5000 pounds of grade A tomatoes and 10,000 pounds of grade B tomatoes, from which they will, make whole canned tomatoes and tomato paste. Whole tomatoes must be composed of at least 80 percent grade A tomatoes, whereas tomato paste must be made with at least 10 percent grade A tomatoes. Whole tomatoes sell for $0.08 per pound and paste sells for $0.05 per pound. Formulate a linear program to solve for how much of each product to make, if the company wants to maximize revenue. (Hint: Let x_WA = pounds of A grade tomatoes used in whole tomatoes, x_WB = pounds of B grade tomatoes used in whole tomatoes; the amount of whole tomatoes produced can be found as x_WA + x_WB after x_WA and x_WB are chosen.)