Homework Chapter $1$ Solve the following Problems. Be sure to use Excel and Word for your work. All work needs to be shown. Problem $1)$ The manager of a small firm is considering whether to produce a new product that would require leasing some special equipment at a cost of $\backslash (\backslash$$ $20,000\backslash )$ per month. In addition to this leasing cost, a production cost of $\backslash (\backslash$$ $10\backslash )$ would be incurred for each unit of the product produced. Each unit sold would generate $\backslash (\backslash$$ $20\backslash )$ in revenue. Develop a mathematical expression for the monthly profit that would be generated by this product in terms of the number of units produced and sold per month. Then determine how large this number needs to be each month to make it profitable to produce the product.

a$)$ solve the problem in the textbook

b$)$ what is the total cost, total revenue and profit if the actual demand is $4000$ units?

c$)$create an excel model for the problems solved in a and b$.$

d$)$how many units should be sold to make a monthly profit of $20\%$ of the monthly lease.

e$)$at what production cost would you be able to breakeven if the monthly demand is $1500$ units?