Vikram Is Planning His Summer Vacation So He Can Maximize $\$ 3.00$

Essay

Vikram is planning his summer vacation so he can maximize his earnings per week. He has an opportunity to mow two types of lawns-household and commercial. Each household takes 1.5 hours to mow and requires $\$ 3.00$ of raw materials (gas, mower rental, etc.). Each commercial job requires 4.0 hours and $\$ 6.00$ worth of raw materials. The maximum number of household jobs available is 10 per week; the maximum number of commercial jobs available is 8 . Having a maximum of 50 hours per week, he wants to take at least 4 household and 3 commercial jobs. He charges $\$ 20.00$ per household and $\$ 40.00$ per commercial lot; variable costs are his only expense. Build a linear programming model to maximize his net contribution per week. Solve the problem using graphical method.