Cheaper by the Dozen (30 points total) For the following questions, assume that: • Total initial costs are $3800. • You can expect to sell 100 items per week if the price is $5 per item. • Sales per week increase by 10 items for every $1 you lower the price. 31. The cost to manufacture one item often decreases as you make more items. For instance, the company providing your printer supplies may give price breaks for larger orders. Suppose that your per-item cost is $3.00, minus $0.01 for every item you manufacture that week. Some examples: Items manufactured 1 10 50 100 Cost per item $2.99 $2.90 $2.50 $2.00 Write an expression for the cost per item when manufacturing x items. Be sure your expression gives the same results as the table. (4 points) 32. Using the cost-per-item expression from question 31, write the cost function C(x) for manufacturing x items. Remember to include the initial costs. Clear any parentheses by using the distributive property. (8 points: 4 points for the initial expression and 4 points for the simplified form)