Please read the short case study attached, formulate the model, solve the two problems in Excel using Solver, and answer the questions in the process. Each question is worth $5$ pts$.$

Son, Ltd$.,$ manufactures a variety of chemical products used by lawn care companies. Son

was recently bought out by a conglomerate, and managers of the two organizations ave

been working together to improve the efficiency of Son's operations.

Managers have been asked to adhere to weekly operating budgets and to develop operating

plans using quantitative methods whenever possible. The manager of one department has

been given a weekly operating budget of $$11,980$ for production of three chemical products,

which for convenience shall be referred to as $Q,R,$ and W $.$ The budget is intended to pay for

direct labor and materials. Processing requirements for the three products, on a per$-$unit

basis, are shown in the table.

The company has a contractual obligation for $85$ units of product R per week.

Material A costs $$4$ per pound, as does material B$.$ Labor costs $$8$ an hour.

Product Q sells for $$122$ a unit, product R sells for $$115$ a unit, and product W sells for $$76$

a unit.

The manager is considering a number of different proposals regarding the quantity of each

product to produce. The manager is primarily interested in maximizing contribution.

Moreover, the manager wants to know how much labor will be needed, as well as the

amount of each material to purchase.

Prepare a report that addresses the following issues:

The optimal quantities of products and the necessary quantities of labor and materials.

One proposal is to make equal amounts of the products. What amount of each will

maximize contribution, and what quantities of labor and materials will be needed? How

much less will total contribution be if this proposal is adopted?