10 & 11 please!

10. A furniture manufacturer makes two types of furniture chairs and sofas. The production of the sofas and chairs requires three operations carpentry, finishing, and upholstery. Manufacturing a chair requires 9 hours of carpentry, 3 hours of finishing, and 2 hours of upholstery. Mamfacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 180 labor hours for carpentry, 66 labor hours for finishing, and 200 labor hours for upholstery. The profit per chair is $20 and the profit per sofa is $35. How many chairs and how many sofas should be produced each day to maximize the profit? What is the maximum profit (a) Set up the linear program, making sure to indicate the inequalities and the objective function. (b) Solve the problem using graphical methods. If you use GeoGebra, (i) be sure to indicate this, (ii) write down what you entered in GeoGebra, (iii) give the solution, and (iv) indicate what points you tried. 11. Jolly the rancher is mixing two types of food, Brand X and Brand Y, for her cattle. Suppose each serving is required to have at least 600 grams of protein, at least 900 grams of minerals, and at least 1500 grams of fat. Brand X has 10 grams of protein, 20 units of minerals, 40 grams of fat, and costs $10 per pound. Brand Y has 30 grams of protein, 20 units of minerals, 30 grams of fat, and costs $12 per pound What is the minimum cost to Jolly Rancher and how many pounds of each type should be used to minimize the cost to Jolly Rancher? (a) Set up the linear program, making sure to indicate the inequalities and the objective function. (b) Solve the problem using graphical methods. If you use GeoGebra, (i) be sure to indicate this, (ii) write down what you entered in GeoGebra, (iii) give the solution, and (iv) indicate what points you tried