1) Project 3 can be selected only if both Projects 1 and 2 are selected, but if both Projects 1 and 2 are selected, Project 3 doesnt have to be selected. The appropriate constraint would be

2) In LP, if the change of the coefficient of a decision variable is within the allowable range for that decision variable, then the optimal objective function value will not change.

3) A company makes two products in a single plant. It runs this plant for 100 hours each week. Each unit of product A that the company produces consumes two hours of plant capacity, earns the company a contribution of $1000, and causes, as undesirable side effects, the emission of 4 ounces of particulates. Each unit of product B that the company produces consumes one hour of capacity earns the company a contribution of $2000, and causes, as undesirable side effects, the emission of 3 ounces of particulates and 1 ounce of chemicals. The EPA (Environmental Protection Agency) requires the company to limit the particulate emission to at most 240 ounces per week and chemical emission to at most 60 ounces per week.

The EPA wants to reduce the release of chemicals into the atmosphere by imposing a fine of $1000 per ounce. Would the government's fine be effective at curbing the release of chemicals?

x3>=x1+x2 x1+x2>=x3 x1>=x3 and x2>=x3 x1+x2+x3