This problem is so hard. I can't figure it out!
"A gaming manufacturing company has developed a new gaming system. To produce the new system, they plan on using resources in two manufacturing plants. The table gives the hours needed for three tasks. For both plants combined, the company has allocated the following resources on a weekly basis: 1700 h of motherboard production, 1800h of technical labor, and 2400 h of general manufacturing. The first plant earns a profit of $90 per gaming system and the second plant earns $70 per system.
Resources Plant 1 (Hours per system) Plant 2 (hours per system) Motherboard Production 9 1 Technical Labor 9 3 General manufacturing 4 8
Use the information above to determine how many gaming systems the company should make in each plant to maximize profit.
1. Create an objective function for the profit P that the company can earn. Let x represent the number of gaming systems that will be made in Plant 1, and let y represent the number of gaming systems that will be made in plant 2.
(My answer - P(x,y)=90x +70y
2. Write a constraint function for each of the resources and for any contextual contraints that you identify.
3.Graph the constraint functions. Then use systems of equations to find the vertex points of the feasibility region.
4. Which vertex point maximizes profit with the given constraints.
5. What is the maximum profit that the company can make with the given constraints? How many gaming systems should each plant make to maximize profit?
I need help with numbers 3, 4, and 5!! :/