help with markets for factors of production

[scarletspider]

An ice cream store hires workers to produce milk shakes. The market for milk shakes is perfectly competitive, and the price of a milk shake is $4. The labour market is competitive, and the wage rate is $40 a day. The table shows the workers total product schedule.

Number of Students........... Quantities of milkshakes (pr day)
1 .....................................................7
2 .....................................................21
3 .....................................................33
4 .....................................................43
5 .....................................................51
6 .....................................................55


a) Calculate the marginal product and the value of the marginal product of the fourth worker.
MP = change TP / Change Labour
MP = 10/1
MP = 10

VMP = MP x P
= 10 x 4
VMP = 40

b) How many workers will the shop hire to maximize profit and how many milk shakes will they produce?
Hire 4 workers since this is when VMP = Wage Rate
Produce 43 milk shakes

c) If the prise rises to $5 per milk shake, how many workers will the shop hire?

d) The shop installs a new machine that increases productivity of the workers by 50%, if the price of a milk shake remains at $4 and the wage rate rises to $48 a day how many workers should be hired?

can someone please help me with questions c and d, Im not sure how I would go about figuring these problems out.

Thanks in advance;-)