$1.$ The demand and supply equations for a commodity are as shown below: Demand: Q$^$d $=7000$ divided by P $+100$ for P $<1000$ & Q$^$d $=0$ for P $>1000$ Supply: Q$^$s $=-0\mathrm{.}3$P $-1$ where P is the market price per unit and Qd and Qs are the quantity demanded and supplied, respectively. Do the following exercises. a$)$ Find the market equilibrium price and quantity. Show the steps you followed to calculate the equilibrium values.

b$)$ Calculate the consumer surplus $($CS$)$ using integration.

c$)$ Calculate the producer surplus $($PS$)$ using integration.

d$)$ Write Python code in Jupyter Notebook to plot the demand and supply curves and illustrate the CS and PS by shading. Use different colours for shading the CS and PS areas, and limit the x$-$axis range for your quantity to between $0$ and $150$ only. Include a screenshot of the code and the generated plot as your answer.